Nate, the question is “how many”, not “is it hard?”
cinquetta
there are 9
PWNAGE
The formula for this is (n+1)^3, where n=pairs of lines stemming from both corners (ie, a triangle with a cross in it has n=1). This triangle has n=3, so it would be (3+1)^3= ~*64*~
MisterH
68.
You forgot the triangles going up the middle PWNAGE.
MisterH
Actually, I’m wrong.
It’s 65.
Kyle
I counted twice and got 70 both times. I’m quite sure of it, but is there any definite answer to be found?
Kyle
I lied, PWNAGE is right, and his calculation makes sense…especially if you go through and count each pattern methodically. You’ll find that you’re counting all your pieces in multiples of 3. That’s a pretty cool calculation, I’ll have to remember to use it from now on.
Sabrie
i count 23? im such a loser boo hoo lolz
Gavin
I probably did this the long way, but I categorised the triangles by the number of ‘pieces’.
1 piece triangle – 7 combos
2 pieces – 12 combos
3 pieces – 10 combos
4 pieces – 13 combos
6 pieces – 8 combos
8 pieces – 6 combos
9 pieces – 3 combos
12 pieces – 4 combos
16 pieces – 1 combo
Total = 64 combinations
I hope that made sense…
Dakota
I got 30……
kjhljhg
38
Dan Gutierrez
This is a triangle with three pairs of interior lines. The general answer for how many triangles there are for a triangle with n pairs of interior lines is (n+1)^3.
So for n = 3 the total = 4^3 = 4*4*4 = 64.
If you add another piar of interior lines then the answer would be for n = 4, so 5^3 = 125, etc…
Actually, I missed a few. I change my answer to 52. Sorry.
Wes
wow that ones actually tricky…i had to stare it for a while saying “wtf? 86? how??” till i figured it out…now i know what nichole and andrew must feel like all the time.
being black is immoral, just throwing that out there.
Most of You got close, You all need to go back and re count it a few times, Not one of you got it right,
74 is the answer.
Kelsie
25
vgvgv hjnufgvhjg
i got like 28
MaryEllen
hmmmm, 76 here
etheoharis
76 is what i got too. I think we are part f the 7.4%
Chris
Matt: How are you sure you’re the one that’s right, when multiple other people got the same result and someone even derived a formula for it… maybe you should do the recounting.
I got 64 btw.
God
It’s hard to believe that it’s only 92.6% of Americans. It’s 14. The entire triangle, the three triangles on the left, the three on the right, the four triangles that two of the six on right and left make up, the two that all three make up, and the triangle on the bottom.
HCH
14?
God
Oh sorry, I lied. It’s actually 64. That is, unless it’s a trick question, and the triangles in the A’s count too. Then it’s 67.
No. It’s definitely 64. I did the math, not using PWNAGE’s formula though. Just found a pretty simple pattern.
David
It’s definitely 64 u guys, and solsta… ur an idiot.
Jake
You guys are i___s. Triangles have 3 SIDES. How many shapes have 3 sides up there?
There are 8 triangles in the picture.
Cory
Hey jake there’s ten smart one. count the triangle you divided into three and count it as one big one. therefore it is ten
jimbob
I counted 50 since Every 3 sided object that can be created in this design is a triangle, there may even be more, LOL.
Carlos
30
c-leb
it is clearly 74, im in a math academy, i can count
mike
what the hell triangles only have 3 sides
its 8
Jean
79, so whats the point of not supplying the answer?
joe mamma
How many triangles are there within a nonagon?
In: Geometry [Edit categories] [Edit]
[Edit]
to calculate the number of possible triangles within a nonagon, one must use combinatorics.
Understand that at first you have to pick the first vertex from 9 points, then the second from eight other possible points, and the third from 7 possible points. And finally that by this process any three vertices could be picked in 6 different orders.
triangles possible are: 9*8*7/6 = 84 possible triangles in a nonagon
Trevor K.
74
hans k
125
reynoldsr13
there’s def. 16
reynoldsr13
srry theres 54
reynoldsr13
now there’s 56
final answer let me know if anybody else gets 56
reynoldsr13
there are 77 srry 4 changing my answer so much this time i double scratch that triple checked
They’d be (10-4)x4x2+(4)x4x1=64 different triangles. Greeting from Sapienza:Università di Roma.
Adam
It’s 8 the others are a dimond of some sort
someone
so quit counting them with the triangles
Adam
Wow u guys are so retarded. No wonder there is such a high percentage of wrong ppl. The answer is 10. There is no formula. The little ones are diamonds. There are 10 triangles. There is no other correct answer so stop wasting ur time trying to seem smart when u really have absolutely no idea.
George
Its 50. No other answer. Ur formulas are stupid. Just count the freakin triangles and ull find that there is 50 triangles. No more, no less. Its 50 and only 50.
Boukje
16, defenitely.. Who knows the correct answer??
Markus Q
Such confidence in assuming that your answer is correct.
You call people names and you still get the answer wrong.
you have to remove the lines and then count how many new ones you got.
I get 79. Here is how I got it. Every triangle uses one of the bottom vertices of the large triangle. Let’s start by considering all triangles that use the bottom right vertex. Look at the triangles that form using a single line emanating from the left bottom vertex of the large triangle.
There are 5 points of intersection, forming 4 segments. You can form a triangle with just the top segment, or the top two segments, the top 3 segments or all 4 segments. There are 3 triangles that can be formed containing the second top most segment but not the top segment.
So the total number of triangles along a segment emanating from one of the segments from the bottom left vertex is 4+3+2+1. Doing this for all four segments gives 10 + 10 +10 + 10 = 40 triangles.
Now reverse roles of the two bottom vertices, counting all triangles that include the left bottom vertex. This gives another 40 triangles. But the whole triangle has been counted twice since it includes both of the bottome vertices of the large triangle, giving 40 + 40 -1 = 79 triangles.
I have to correct my previous answer. There are four triangles along each segment from the other vertex that is double counted. So that would give 40 + 40 – 16 = 64 triangles. I don’t see any additional triangles. What am I missing?
Good Job guys. Really, obviously, it’s 64.
But for those who do not understand WHY it is because of the formula, i’m gonna explain it to you.
First, let’s give names to summit of the triangle:
A for the upper one;
B for the lower left one;
C last but not least upper right.
Second, you oughta admit that in order to have a triangle, there are two possibilities:
– B and C are in this triangle
– B or C is in this triangle
(A is not necessary in this demonstration ^^)
So, let’s count triangles having B and C in their summits.
In fact, it’s the easiest part !
You just have to cout all the dots created by 2 lines crossed (execpt B and C obviously)
And you can notice that you have 4*4 dots
That’s to say (3+1)*(3+1) … that’s (n+1)^2 dots for a first time
Next let’s count triangles with only B (those with only C are as numerous as those one for a question of symetry)
i.e. 2*Triangle(having B) = Triangle(having B or C)
So here, it’s more complicated, but here we go.
Let’s take a line incoming from C and cutting the lines from B …
We can have 3+2+1 = 6 triangles on this line
And … we have (3+1) lines like this
So … (3+1)*(3+2+1) triangles with only B
With n lines, we have so (n+1)*(n+ … + 2 +1) triangles with B
Or (n + … + 2 + 1) = n * (n + 1) / 2
(google that if you do not believe ^^)
So we have (n+1)*(n+1)*n/2 triangles with B
That’s to say we have n*((n+1)^2) triangles with B or C
Counting all the triangles, we have:
(n+1)^2 + n((n+1)^2)
= ((n+1)^2) * (1 + n)
That’s to say (n+1)^3 … (hope you will understand that 64 is the answer :p)
If you’re still sceptic, try with n = 0,1,2 … (you’ll find 1, 8, 27 if you’re smart enough)
l!v!3
EVERYONE IS WRONG THE ANSWER IS 1 DUHH ITS VERY SIMPLE…… WHENI LOOK AT IT I SEE ONE TRIANGLE…RETARDSS IM 12 ND I GOT IT RIGHT (I DONT FEEL LKIKE COUNTING HEHE IM LAZY)
Nick
Yea… It’s definately 64… I seriously cannot believe the stubbornness of what I can only hope are a bunch of 7 year olds posting here… It takes no longer than a minute to count at LEAST half of the 64… If you want more proof…go to the site posted above… I’ll post it for anyone who can’t find it…. It literally shows you each triangle one by one… You don’t even have to worry about doing math…
heugbstrklhbuaehna,hbakhbae tbhtyr agh bugdalb uael h ghkfdmc
64 I know it is right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
nun ov ya bizness
i say 8
jarjar
I’m not sure if anyone still cares, but the answer is 22 three-sided polygons….ahem, “triangles”. This is assuming that you are only looking at the big triangle and are not using anything else but your eyes!
Derfaulenzer
I take the question to mean how many *types* of triangles are present in the diagram. In that case, there are three: scalene, isosceles, and equilateral. 😉
Ok, I don’t think that was the real question, but really folks. Trust the formula. The answer is 64.
Nick
Jarjar… You’re an i_i_t… Did you (does anyone) read any previous posts?
kayte
27
Allie
You guys do realize a triangle has 3 sides, right? There are a total of 10 triangles. You guys are making a big deal about it with all the formulas and such. There are 10 look,
You see the three lines on each side of the triangle (Inside the triangle)
Add those together you get 6
Then right next to those is another triangle which equals 7
Then the big triangle which all the lines are in makes 8
Remeber the lines I mentioned above, those are inside triangles. (2)
8+2=10!
I’ve just read comments, it’s not 64 at all I counted 86 and maybe it will be more
rschwarze
hey guys this may seem strange but i got 87 in my counting. no math just counting
AJ
I got 72
Meagan
I got 26
Zach
its 64
cchhaarrrllllliiiiiii
it is 40 i have taken the test a school even i got the question right and i am 13 ffs you are all brain deadd lol!!!!
Cliff
Surely its 10 including the main triangle they are all inside!
There’s only diamonds in the upper half !
Cliff
Or actually 12 🙂
Cliff
or actually loads of them …aahhh loads and loads !!
mohammed
58
BAKING
I counted 8, then 10, then like 20-something, now 50.
I am almost 100% sure there are only 50.
BAKING
Yep, official answer is 50. I can’t see anymore out of the diagram… And there are 25 points where 2 straight lines overlap eachother inside the biggest triangle. 25 x 2 = 50, I counted 50 so I guarentee there are only 50.
BAKING
Ahhhhhh nevermind I see the rest of them now… Crap hold on.
BAKING
I was wrong 🙁 64 triangles.
joe
you guys are stupid its 64
joe
you cant split the diamonds in half….
Adelyn Lorain-Dyersburg, TN
i got 41.
i cant find anymore than that.
so how are you getting 64?
IDIOTS ^.^
Its 763 IDIOTS.
BTW.
“Im from Harvard University”
-Notice the tinge of Sarcasm?
Lee
Solution is definitely 64, a friend and I counted this and both 64 if you want to count this properly this one helped out because of the coloring.
its got to be 64, and how are you idiots getting 8, why dont you try thinking outside the box for a change
Jessica Isabella.
if you count the capital A’s there are 11 =]
hehehe… yeah,
… you people make me confused… i thought triangles had 3 sides. i don’t see any other 3 sided shapes… apart from the actual big triangle and the seven other smaller triangles… + the three capital A’s in MANY, TRIANGLES && American’s..
where are people getting all these big numbers from!?!?
Hmf.. difficult people.
Jessica Isabella.
OH… nah you guyz cant count ‘triangles’ that have lines going through them… coz that makes them therfor NOT a triangle… tri = 3 ,people!! 3 sides!! not three sides + lines go through them.
gees.. you people made it real hard on yourselves including thoughs non triangles.
coz therez HEAPS of them!! lol. =]
Jessica Isabella.
oh wait… then i say 10.. coz the big one has lines through it&&im sticking to my lazy theory… =]
lol
a lot.
psw259
69
Hunter
This thread is totally hilarious. My favorite is when people post an answer they are DEFINITELY sure about, then continue to revise their answer 4 or 5 times with increasing degrees of certainty!!
>>James Says:
>>June 12th, 2009 at 9:00 pm
>>
>> way i found 4 more 38 HAHAHAHHA OKAY NO MORE
>>LOOKING THAT IS MY FINAL FINAL END OF THE WORLD
>>ANSWER AND IT IS RIGHT. 38 I AM SO SURE.
If someone wanted a REAL challenge, they should actually go through this thread and count the number of posters who got it right on their first post to see if it was actually close to 92.6%… I’m guessing it would be. (btw I’m purposely not posting the answer I think is right – it appears many times above.)
malcolm laraque
there are 10 TRIANGLES
malcolm laraque
never mind im a retard maybe there is 27.. I DONT KNOW
Does anyone notice the *obvious* 9 Quadrilaterals in the picture, Yah… those 4 sided objects in the center have a shocking *4* sides. Any formula that includes them into the equation is already incorrect. I see why it says 92.6% of Americans get this wrong.
I counted 58 but i belive that there is more triangles.
stefon
theres 1 triangle
stefon
nevermind theres 3 if u can see it
Angie
11…
Funkydunk
So what is the right answer?
Last time I checked, a triangle was still roughly described as:
“A 3 sided shape (3 corners) in which the sum of all internal angles = 180 Deg and the sum of all external angles = 360 Deg.”
So unless my eyes are playing tricks on me there are 8 triangles in the pic. I cant understand how some ppl are finding more than 8 if a triangle has to have 3 (and only 3) sides.
Please enlighten me as to how I can find more than 8 in the pic.
Funkydunk
I can see what ppl mean by there being another 2 at the bottom, but im not fully convinced as they are interupted by other lines.
i think theres about 30/40 i keep losing track ! <333 xxxx
ambax4
12??
gm
21
matt
67;D
Sammy
There was someone who complained that “Triangles with lines going through them are not triangles”. I’m afraid you’re wrong. A shape with 3 sides is a triangle regardless of the pattern or lines on the inside. The standard answer would be that there are 8 triangles. The 7 at the bottom and the entire shape itself, however each of the bottom 7 triangles can be added to each other to make slightly bigger triangles. Then if you realise that the bottom line of the big triangle connected to all of the intersections make triangles too which can then be added to each other… there are lots lots lots lots (as the trolls would put it).
There was someone who complained that “Triangles with lines going through them are not triangles”. I’m afraid you’re wrong. A shape with 3 sides is a triangle regardless of the pattern or lines on the inside. The standard answer would be that there are 8 triangles. The 7 at the bottom and the entire shape itself, however each of the bottom 7 triangles can be added to each other to make slightly bigger triangles. Then if you realise that the bottom line of the big triangle connected to all of the intersections make triangles too which can then be added to each other… there are lots lots lots lots (as the trolls would put it).
Jessica
ok, i got 16 triangles ^_^
anybody get the same??
Jessica
i got 343 triangles
(n+1)^3 n=number of lines in the triangle (6)
(6+1)^3
(7)^3
7x7x7
343
Jessica
ok, i got 16 triangles ^_^
anybody get the same??
Jessica
sorry 🙁
sent the answer twice by mistake
lol
ronie
4+9+9+20+20=62
felix
68
Riana
I get 72 triangels
Riana
I got 72 triangles
RANDOMperson
I got 28?
RANDOMperson
oops i got 62 now…. i prabably missed 2 so i would say 64, acording to the number of combinations and mathimatical thinking, 64 should be right!
famethyst
my comment there are 15 triangles and im from england
Dini
58 but I’ll try to count them again, hahaha…
Cloud
got 64 here -____-
Osin
64 triangle
rahbudi
60 !!!
Samantha
I say there are at least 74, but i could be wrong. I know for a fact that there is 1 duh!!
Samantha
I think im one of those 92.6% of all Americans with this question…
Bilbo
I agree with the person from england (famthyst).
Okay, there is the entire triangle.
Then, look at the 4 big shapes within the triangle. 3 of them are triangles
That makes 4.
Then, Look at the 2 triangles that sort of add on to the triangle at the base.
That makes 6.
Now, look at the 6 tiny triangles within the 2 triangles at the right and left.
That makes 12
Finally, look at the 3 capital A’s, all with triangles
That makes 15 triangles.
I’m an American by the way. (who’s 11)
luke office
there is obviously 8 in there. there is 3 lined in a triangle not 4 deer
Well it all depends on what the image is asking for. How many triangles? Well since it is not specific, lets assume it means ALL TYPES of triangles including Equilateral, Isosceles, Right and Scalene Triangles. Now in other “Count The Triangles” images, it asks how many. Now They include all triangle shapes. If it makes three sides, IT MAKES A TRIANGLE. Regardless if a line passes through a triangle, if another triangle is made, IT is still a triangle. With all this in mind if you count using this method, there are in fact 64 Triangles.
As far as if you were only going to count JUST ISOSCELES or EQUILATERAL or TRUE TRIANGLES (excluding triangles with lines passing through them), or JUST SCALENE TRIANGLES! Then the number changes, but lets not kid ourselves, and count all damn possible triangles!
The image simply states “How many Triangles” If it forms a triangle from three interconnecting lines, alas it is a triangle.
like luke office said there frigin 8. plus im british so im right
jusnan
127
froggie
56……I am french, so I can’t be wrong 🙂
Lucas
64.
Yes, this is absolutely right. The easiest way to count is to isolate 2 points (for example, the 2 from the base) and see how many do you get adding a third point. Doing this with the base line, you get 16. After that, use one of the vertices from the base line and get the second vertice from one of the first lines above the base one.
All triangles will have at least one vertice from the base line.
froggie
Lucas, you are rigth and I was wrong. I did the couting again and I found 64 triangles. So, I am french and I was wrong….what a shame.
How I count :
Let name A and B the two vertices on the base.
A triangle contain A alone, or B alone ,or A and B.
I make 2 disjoint classes to be sure not to count twice the same triangle :
-First I count the triangles containing A alone with those containing A and B.
I found 40 triangles.
-Then I count the triangles containing B but not A.
I found 24 triangles.
So 64 triangles is correct.
Thank you Lucas to open my eyes…..
ME
10 . . . alot of them arn’t triangles. . . there is the big triangle, then there is three at the bottom, and then there is three in two of them and 3 + 3 + 3 + 1 = 10
Bilbo
Whoa, I got 64! I missed a lot the first time….
Bilbo
And I didn’t even look at the comments saying “I got 64”.
Bilbo
Oops, I mean 65 (counting the triangle in Americans).
Bilbo
66, I forgot the word “TriAngles.
Bilbo
67. I forgot yet another A…
marsinjo
insya allah jawaban yang paling bener itu 8 segitiga,yakinlah sumpah……
zumpaaahh ‘ane zuzur,
I think there are 64 triangles < who else does because i'm not american and i'm not dum!!!!!!!!!!!!!!!!!
Lucas Madeira
8
husnul
The answers is 64 triangle
pattystomper
I counted 76 triangles.
joyce
there are only 10. others are not triangles dont make it hard folks its so simple. there are only ten, dont count the entire triangle repeatedly.
American boii
Ohkay, here’s the deal….. YOU ARE ALL RETARDED!!!!!!!!!!! There are clearly 29 triangle… i don’t see why we are all fighting oer how many triangles there are…. I think that it is impossible to have 60 or 64 triangles…… You are all stupid….. Btw I’m 15….. hahahhaha
I found it 16 triangles at the first time, but I believe that the correct answer is 64. I’m still counting.
die art
36×2+4
Lee
i found 80
i really wanna know the correct answer >_<
indo
72
nana
I think 64 is the right answer!! Please tell me the answer cos I really wanna know
bachem
soo what is the right answer? ^_^
Billy
80
sibolang
whoever said 76, we are on the same page..yeeha..
equation:
(4*10*2)-4 = 76
the first 4 means there is 4 “big” triangle,
then there is 10 “small” triangle each,
2 means reflecting right and left
-4 means substracting the duplication (4 triangle in the middle).
Yeah I know…only me who can understand what im talkin bout..
I got 76 too. But i solved it in a different way.big ones are 16*2 = 32 – 4 because big triangles are repeated = 28. Small by 1’s triangles = 12*2 = 24. Small by 2’s triangles is 8*2 = 16 then small by 3’s triangle is 4*2= 8 28+24+16+8 = 76 🙂
henny
i got 76
Jan
I have 64.. Maybe you count tetrahedrons, or counting something two times?
Got 76 then googled it. Photobucket has a pic confirming 64 that the last figure should say 4•3•2. Thoughts?
Lee
I counted 198. Let’s start by following the lowest line going up to the right. There are 4 segmented triangles, but combined into double segments, there are 3 more. Combined into triple segments, there are two. And combined as a quadruple segment, there’s 1. So 4+3+2+=10 now there are four segments like that separated by lines going up to the right. So it’s 40+30+20+10=100. Now repeat for the other side. 100+100 = 200. This number accounts for 2 instances of the largest internal triangle at the base and the triangle comprised of the entierty of the shape. Subtract one of each instance. 200-2=198.
Lin
So this is over a year old and people are still posting. what’s the answer?
annihilat0rbd
i found 74 .. [bangladeshi]
Randall
You’re all blind… first, there’s no mathematic equation that applies, because permutations don’t exist at all three points, so you can throw that one right out the window. If you simply use your eyes and your brain, it’s simple to come up with the right answer which is 40… no more, no less…
Vee
There are 14 triangles!!
anup
can any 1 tell me the ri8 answer
John
There are 74.
Sierra
64! Use your eyes.. Lol 16 off the main base and 48 little ones coming out of the corners…
ahmed
intially i got 76, but dan again i got 79 again. Am frm somalia
ahmed
its 79, am da genious frm somalia
Sulldrian’s Class
My 6th grade math class got 60!! We counted the triangles in the A’s and the word triangle! =)
Kucing Garong
Only One triangle, the other triangles are its friends….
– Start from bottom left corner, top (or first) column. In that column alone you can make four different triangles (corner to first “cross” line, corner to second “cross” line…).
– Repeat for the other columns. You should get 16.
– Now we make wider triangles out of TWO columns, still from the bottom left corner. You can find 12 more this way.
– Do the same thing with three columns (8 more) and four columns (4 more).
– We now have 40 triangles. We can repeat the same process from the right, but we CANNOT count triangles that touch the left corner (basically we can’t use the bottom column), as we have counted them already. You should get 24 more, a total of 64.
321 responses to “How Many Triangles Are There in This Picture? | 92.6% of Americans Get This Question Wrong [PIC]”
8
I got 44
i got 53 trangles
23??
now i got 16 =_=
in the triangle, there are little ones….then the the littler ones form bigger ones people…so easy
Nate, the question is “how many”, not “is it hard?”
there are 9
The formula for this is (n+1)^3, where n=pairs of lines stemming from both corners (ie, a triangle with a cross in it has n=1). This triangle has n=3, so it would be (3+1)^3= ~*64*~
68.
You forgot the triangles going up the middle PWNAGE.
Actually, I’m wrong.
It’s 65.
I counted twice and got 70 both times. I’m quite sure of it, but is there any definite answer to be found?
I lied, PWNAGE is right, and his calculation makes sense…especially if you go through and count each pattern methodically. You’ll find that you’re counting all your pieces in multiples of 3. That’s a pretty cool calculation, I’ll have to remember to use it from now on.
i count 23? im such a loser boo hoo lolz
I probably did this the long way, but I categorised the triangles by the number of ‘pieces’.
1 piece triangle – 7 combos
2 pieces – 12 combos
3 pieces – 10 combos
4 pieces – 13 combos
6 pieces – 8 combos
8 pieces – 6 combos
9 pieces – 3 combos
12 pieces – 4 combos
16 pieces – 1 combo
Total = 64 combinations
I hope that made sense…
I got 30……
38
This is a triangle with three pairs of interior lines. The general answer for how many triangles there are for a triangle with n pairs of interior lines is (n+1)^3.
So for n = 3 the total = 4^3 = 4*4*4 = 64.
If you add another piar of interior lines then the answer would be for n = 4, so 5^3 = 125, etc…
there are 9
86
I get 10. *shrugs*
Actually, I missed a few. I change my answer to 52. Sorry.
wow that ones actually tricky…i had to stare it for a while saying “wtf? 86? how??” till i figured it out…now i know what nichole and andrew must feel like all the time.
being black is immoral, just throwing that out there.
it’s 64 ^^
Most of You got close, You all need to go back and re count it a few times, Not one of you got it right,
74 is the answer.
25
i got like 28
hmmmm, 76 here
76 is what i got too. I think we are part f the 7.4%
Matt: How are you sure you’re the one that’s right, when multiple other people got the same result and someone even derived a formula for it… maybe you should do the recounting.
I got 64 btw.
It’s hard to believe that it’s only 92.6% of Americans. It’s 14. The entire triangle, the three triangles on the left, the three on the right, the four triangles that two of the six on right and left make up, the two that all three make up, and the triangle on the bottom.
14?
Oh sorry, I lied. It’s actually 64. That is, unless it’s a trick question, and the triangles in the A’s count too. Then it’s 67.
theres 1
17???
52
15
26 triangles
49 triangles now
51 now
i think 8 or 24 i am 11 and still smarter than all yall 8^)
by the way im correct i gradguated like most of you didnt you guys dont know how to count
any one there
there r 32
i think there are 8….DUH!!!
41 u all r retarded
40 u all r not math professers
s l
faggots it’s 200
No. It’s definitely 64. I did the math, not using PWNAGE’s formula though. Just found a pretty simple pattern.
It’s definitely 64 u guys, and solsta… ur an idiot.
You guys are i___s. Triangles have 3 SIDES. How many shapes have 3 sides up there?
There are 8 triangles in the picture.
Hey jake there’s ten smart one. count the triangle you divided into three and count it as one big one. therefore it is ten
I counted 50 since Every 3 sided object that can be created in this design is a triangle, there may even be more, LOL.
30
it is clearly 74, im in a math academy, i can count
what the hell triangles only have 3 sides
its 8
79, so whats the point of not supplying the answer?
How many triangles are there within a nonagon?
In: Geometry [Edit categories] [Edit]
[Edit]
to calculate the number of possible triangles within a nonagon, one must use combinatorics.
Understand that at first you have to pick the first vertex from 9 points, then the second from eight other possible points, and the third from 7 possible points. And finally that by this process any three vertices could be picked in 6 different orders.
triangles possible are: 9*8*7/6 = 84 possible triangles in a nonagon
74
125
there’s def. 16
srry theres 54
now there’s 56
final answer let me know if anybody else gets 56
there are 77 srry 4 changing my answer so much this time i double scratch that triple checked
64. final answer.
C:1+1+1+1=4
L: 6+6+6+6=24
R: 6+6+6+6=24
CL:3+2+1=6
CR:3+2+1=6
Total:4+24+24+6+6=64
C=centre; L=left; R=right
23
theres ONE. always making things harder than they should be.
57
First count I get 70
44
They’d be (10-4)x4x2+(4)x4x1=64 different triangles. Greeting from Sapienza:Università di Roma.
It’s 8 the others are a dimond of some sort
so quit counting them with the triangles
Wow u guys are so retarded. No wonder there is such a high percentage of wrong ppl. The answer is 10. There is no formula. The little ones are diamonds. There are 10 triangles. There is no other correct answer so stop wasting ur time trying to seem smart when u really have absolutely no idea.
Its 50. No other answer. Ur formulas are stupid. Just count the freakin triangles and ull find that there is 50 triangles. No more, no less. Its 50 and only 50.
16, defenitely.. Who knows the correct answer??
Such confidence in assuming that your answer is correct.
You call people names and you still get the answer wrong.
you have to remove the lines and then count how many new ones you got.
So those so called diamonds are now a triangle.
it is more than 64 and less than 100!
I get 79. Here is how I got it. Every triangle uses one of the bottom vertices of the large triangle. Let’s start by considering all triangles that use the bottom right vertex. Look at the triangles that form using a single line emanating from the left bottom vertex of the large triangle.
There are 5 points of intersection, forming 4 segments. You can form a triangle with just the top segment, or the top two segments, the top 3 segments or all 4 segments. There are 3 triangles that can be formed containing the second top most segment but not the top segment.
So the total number of triangles along a segment emanating from one of the segments from the bottom left vertex is 4+3+2+1. Doing this for all four segments gives 10 + 10 +10 + 10 = 40 triangles.
Now reverse roles of the two bottom vertices, counting all triangles that include the left bottom vertex. This gives another 40 triangles. But the whole triangle has been counted twice since it includes both of the bottome vertices of the large triangle, giving 40 + 40 -1 = 79 triangles.
I have to correct my previous answer. There are four triangles along each segment from the other vertex that is double counted. So that would give 40 + 40 – 16 = 64 triangles. I don’t see any additional triangles. What am I missing?
Solution: 64
http://www.iwpcug.org/davidbro/puz0603.htm
I counted 27 triangles
oops counted again and there are definitely 32 triangles
ahh okay i found 2 more my FINAL answer is 34 triangles that is THE answer
no way i found 4 more 38 HAHAHAHHA OKAY NO MORE LOOKING THAT IS MY FINAL FINAL END OF THE WORLD ANSWER AND IT IS RIGHT. 38 I AM SO SURE.
31
64
76
oops! i counted the 9 small quads. sorry, it’s 64
I counted 12
68 triangles.
i counted way off there are 64
Good Job guys. Really, obviously, it’s 64.
But for those who do not understand WHY it is because of the formula, i’m gonna explain it to you.
First, let’s give names to summit of the triangle:
A for the upper one;
B for the lower left one;
C last but not least upper right.
Second, you oughta admit that in order to have a triangle, there are two possibilities:
– B and C are in this triangle
– B or C is in this triangle
(A is not necessary in this demonstration ^^)
So, let’s count triangles having B and C in their summits.
In fact, it’s the easiest part !
You just have to cout all the dots created by 2 lines crossed (execpt B and C obviously)
And you can notice that you have 4*4 dots
That’s to say (3+1)*(3+1) … that’s (n+1)^2 dots for a first time
Next let’s count triangles with only B (those with only C are as numerous as those one for a question of symetry)
i.e. 2*Triangle(having B) = Triangle(having B or C)
So here, it’s more complicated, but here we go.
Let’s take a line incoming from C and cutting the lines from B …
We can have 3+2+1 = 6 triangles on this line
And … we have (3+1) lines like this
So … (3+1)*(3+2+1) triangles with only B
With n lines, we have so (n+1)*(n+ … + 2 +1) triangles with B
Or (n + … + 2 + 1) = n * (n + 1) / 2
(google that if you do not believe ^^)
So we have (n+1)*(n+1)*n/2 triangles with B
That’s to say we have n*((n+1)^2) triangles with B or C
Counting all the triangles, we have:
(n+1)^2 + n((n+1)^2)
= ((n+1)^2) * (1 + n)
That’s to say (n+1)^3 … (hope you will understand that 64 is the answer :p)
If you’re still sceptic, try with n = 0,1,2 … (you’ll find 1, 8, 27 if you’re smart enough)
EVERYONE IS WRONG THE ANSWER IS 1 DUHH ITS VERY SIMPLE…… WHENI LOOK AT IT I SEE ONE TRIANGLE…RETARDSS IM 12 ND I GOT IT RIGHT (I DONT FEEL LKIKE COUNTING HEHE IM LAZY)
Yea… It’s definately 64… I seriously cannot believe the stubbornness of what I can only hope are a bunch of 7 year olds posting here… It takes no longer than a minute to count at LEAST half of the 64… If you want more proof…go to the site posted above… I’ll post it for anyone who can’t find it…. It literally shows you each triangle one by one… You don’t even have to worry about doing math…
http://www.iwpcug.org/davidbro/puz0603.htm
64 I know it is right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
i say 8
I’m not sure if anyone still cares, but the answer is 22 three-sided polygons….ahem, “triangles”. This is assuming that you are only looking at the big triangle and are not using anything else but your eyes!
I take the question to mean how many *types* of triangles are present in the diagram. In that case, there are three: scalene, isosceles, and equilateral. 😉
Ok, I don’t think that was the real question, but really folks. Trust the formula. The answer is 64.
Jarjar… You’re an i_i_t… Did you (does anyone) read any previous posts?
27
You guys do realize a triangle has 3 sides, right? There are a total of 10 triangles. You guys are making a big deal about it with all the formulas and such. There are 10 look,
You see the three lines on each side of the triangle (Inside the triangle)
Add those together you get 6
Then right next to those is another triangle which equals 7
Then the big triangle which all the lines are in makes 8
Remeber the lines I mentioned above, those are inside triangles. (2)
8+2=10!
The answer is 19
Wow a triangle is a 3 sided figure there are nine 3 sided figures in this picture.. meaning all the rest of the them are NOT triangles.. i win?
acually 10 3 sided figures
its either 12342153 or 9
I’m not sure, I’ve not explored for a long time, but I got 60 triangles. And where can I see the correct answer?
I saw now It is 64 😛 maybe i will find more
I’ve just read comments, it’s not 64 at all I counted 86 and maybe it will be more
hey guys this may seem strange but i got 87 in my counting. no math just counting
I got 72
I got 26
its 64
it is 40 i have taken the test a school even i got the question right and i am 13 ffs you are all brain deadd lol!!!!
Surely its 10 including the main triangle they are all inside!
There’s only diamonds in the upper half !
Or actually 12 🙂
or actually loads of them …aahhh loads and loads !!
58
I counted 8, then 10, then like 20-something, now 50.
I am almost 100% sure there are only 50.
Yep, official answer is 50. I can’t see anymore out of the diagram… And there are 25 points where 2 straight lines overlap eachother inside the biggest triangle. 25 x 2 = 50, I counted 50 so I guarentee there are only 50.
Ahhhhhh nevermind I see the rest of them now… Crap hold on.
I was wrong 🙁 64 triangles.
you guys are stupid its 64
you cant split the diamonds in half….
i got 41.
i cant find anymore than that.
so how are you getting 64?
Its 763 IDIOTS.
BTW.
“Im from Harvard University”
-Notice the tinge of Sarcasm?
Solution is definitely 64, a friend and I counted this and both 64 if you want to count this properly this one helped out because of the coloring.
http://www.iwpcug.org/davidbro/puz0603.htm I can see that the % of people that get this wrong is also true, look at the answers people are giving. LOL
its got to be 64, and how are you idiots getting 8, why dont you try thinking outside the box for a change
if you count the capital A’s there are 11 =]
hehehe… yeah,
… you people make me confused… i thought triangles had 3 sides. i don’t see any other 3 sided shapes… apart from the actual big triangle and the seven other smaller triangles… + the three capital A’s in MANY, TRIANGLES && American’s..
where are people getting all these big numbers from!?!?
Hmf.. difficult people.
OH… nah you guyz cant count ‘triangles’ that have lines going through them… coz that makes them therfor NOT a triangle… tri = 3 ,people!! 3 sides!! not three sides + lines go through them.
gees.. you people made it real hard on yourselves including thoughs non triangles.
coz therez HEAPS of them!! lol. =]
oh wait… then i say 10.. coz the big one has lines through it&&im sticking to my lazy theory… =]
a lot.
69
This thread is totally hilarious. My favorite is when people post an answer they are DEFINITELY sure about, then continue to revise their answer 4 or 5 times with increasing degrees of certainty!!
>>James Says:
>>June 12th, 2009 at 9:00 pm
>>
>> way i found 4 more 38 HAHAHAHHA OKAY NO MORE
>>LOOKING THAT IS MY FINAL FINAL END OF THE WORLD
>>ANSWER AND IT IS RIGHT. 38 I AM SO SURE.
If someone wanted a REAL challenge, they should actually go through this thread and count the number of posters who got it right on their first post to see if it was actually close to 92.6%… I’m guessing it would be. (btw I’m purposely not posting the answer I think is right – it appears many times above.)
there are 10 TRIANGLES
never mind im a retard maybe there is 27.. I DONT KNOW
http://www.iwpcug.org/davidbro/puz0603.htm
its 68 you guys are all missing the middle triangles including the one that forms it all
I guess 67, but I lost count at 47, and kept on counting, this was a great way to waist 5mins.
Does anyone notice the *obvious* 9 Quadrilaterals in the picture, Yah… those 4 sided objects in the center have a shocking *4* sides. Any formula that includes them into the equation is already incorrect. I see why it says 92.6% of Americans get this wrong.
16
igot 11
OMG!How its could be 64?you do not think the general image and the bottom. one word – the Americans. So there are 66
Stop.70 now O_O
Ok.I’m serious now.and recent decision is 78.
The answer is 64.
(n+1)^3, n= number of lines in the triangle = 3
(3+1)^3
4^3=64
50
whoops, i meant 64
its 30 i m sure
It is 30. =) and i am not a genius=)
From South Africa the answer is 64
im no genius but i count 8
Its way more than 8!!!
I counted 8 but I think there are more some way or another
no i change my mind there are 20
There is only one triangle.
i count 52, might have missed some.
There’s 8 and you have to believe me cause I’m Albert Einstein.
64.
yea i counted 64
pretty sure its 68 could be more
I found 64. hmm.
i am a genius there are 8
i counted 39… or maybe 40 im not counting again!
I counted 10 triangles
i counted 30 i have no idea were i got dat xxx <3
no chance 64 theres about 21 dur brains
76
13
I counted 58 but i belive that there is more triangles.
theres 1 triangle
nevermind theres 3 if u can see it
11…
So what is the right answer?
Last time I checked, a triangle was still roughly described as:
“A 3 sided shape (3 corners) in which the sum of all internal angles = 180 Deg and the sum of all external angles = 360 Deg.”
So unless my eyes are playing tricks on me there are 8 triangles in the pic. I cant understand how some ppl are finding more than 8 if a triangle has to have 3 (and only 3) sides.
Please enlighten me as to how I can find more than 8 in the pic.
I can see what ppl mean by there being another 2 at the bottom, but im not fully convinced as they are interupted by other lines.
i say 8
i count 8
the solution is here:
http://www.iwpcug.org/davidbro/puz0603.htm
(64)
i think theres about 30/40 i keep losing track ! <333 xxxx
12??
21
67;D
There was someone who complained that “Triangles with lines going through them are not triangles”. I’m afraid you’re wrong. A shape with 3 sides is a triangle regardless of the pattern or lines on the inside. The standard answer would be that there are 8 triangles. The 7 at the bottom and the entire shape itself, however each of the bottom 7 triangles can be added to each other to make slightly bigger triangles. Then if you realise that the bottom line of the big triangle connected to all of the intersections make triangles too which can then be added to each other… there are lots lots lots lots (as the trolls would put it).
64 is the correct answer.
8 because other dont have 3 sides 0-0
we think there are at least 74 triangles. we know this for a fact because we’re brilliant and we worked this out with the teacher. <3<3
oops typo! we mean 64 😉
there are 16 traingles
There was someone who complained that “Triangles with lines going through them are not triangles”. I’m afraid you’re wrong. A shape with 3 sides is a triangle regardless of the pattern or lines on the inside. The standard answer would be that there are 8 triangles. The 7 at the bottom and the entire shape itself, however each of the bottom 7 triangles can be added to each other to make slightly bigger triangles. Then if you realise that the bottom line of the big triangle connected to all of the intersections make triangles too which can then be added to each other… there are lots lots lots lots (as the trolls would put it).
ok, i got 16 triangles ^_^
anybody get the same??
i got 343 triangles
(n+1)^3 n=number of lines in the triangle (6)
(6+1)^3
(7)^3
7x7x7
343
ok, i got 16 triangles ^_^
anybody get the same??
sorry 🙁
sent the answer twice by mistake
lol
4+9+9+20+20=62
68
I get 72 triangels
I got 72 triangles
I got 28?
oops i got 62 now…. i prabably missed 2 so i would say 64, acording to the number of combinations and mathimatical thinking, 64 should be right!
my comment there are 15 triangles and im from england
58 but I’ll try to count them again, hahaha…
got 64 here -____-
64 triangle
60 !!!
I say there are at least 74, but i could be wrong. I know for a fact that there is 1 duh!!
I think im one of those 92.6% of all Americans with this question…
I agree with the person from england (famthyst).
Okay, there is the entire triangle.
Then, look at the 4 big shapes within the triangle. 3 of them are triangles
That makes 4.
Then, Look at the 2 triangles that sort of add on to the triangle at the base.
That makes 6.
Now, look at the 6 tiny triangles within the 2 triangles at the right and left.
That makes 12
Finally, look at the 3 capital A’s, all with triangles
That makes 15 triangles.
I’m an American by the way. (who’s 11)
there is obviously 8 in there. there is 3 lined in a triangle not 4 deer
14
OK, who’s counting diamonds?? Oh, what was that mathematical term for diamonds?!?!??!
Well it all depends on what the image is asking for. How many triangles? Well since it is not specific, lets assume it means ALL TYPES of triangles including Equilateral, Isosceles, Right and Scalene Triangles. Now in other “Count The Triangles” images, it asks how many. Now They include all triangle shapes. If it makes three sides, IT MAKES A TRIANGLE. Regardless if a line passes through a triangle, if another triangle is made, IT is still a triangle. With all this in mind if you count using this method, there are in fact 64 Triangles.
As far as if you were only going to count JUST ISOSCELES or EQUILATERAL or TRUE TRIANGLES (excluding triangles with lines passing through them), or JUST SCALENE TRIANGLES! Then the number changes, but lets not kid ourselves, and count all damn possible triangles!
The image simply states “How many Triangles” If it forms a triangle from three interconnecting lines, alas it is a triangle.
I Found 2 lolz,
THIS CANT BE DONE!
I counted 76 triangles. (do I win a ham?)
there is 33
like luke office said there frigin 8. plus im british so im right
127
56……I am french, so I can’t be wrong 🙂
64.
Yes, this is absolutely right. The easiest way to count is to isolate 2 points (for example, the 2 from the base) and see how many do you get adding a third point. Doing this with the base line, you get 16. After that, use one of the vertices from the base line and get the second vertice from one of the first lines above the base one.
All triangles will have at least one vertice from the base line.
Lucas, you are rigth and I was wrong. I did the couting again and I found 64 triangles. So, I am french and I was wrong….what a shame.
How I count :
Let name A and B the two vertices on the base.
A triangle contain A alone, or B alone ,or A and B.
I make 2 disjoint classes to be sure not to count twice the same triangle :
-First I count the triangles containing A alone with those containing A and B.
I found 40 triangles.
-Then I count the triangles containing B but not A.
I found 24 triangles.
So 64 triangles is correct.
Thank you Lucas to open my eyes…..
10 . . . alot of them arn’t triangles. . . there is the big triangle, then there is three at the bottom, and then there is three in two of them and 3 + 3 + 3 + 1 = 10
Whoa, I got 64! I missed a lot the first time….
And I didn’t even look at the comments saying “I got 64”.
Oops, I mean 65 (counting the triangle in Americans).
66, I forgot the word “TriAngles.
67. I forgot yet another A…
insya allah jawaban yang paling bener itu 8 segitiga,yakinlah sumpah……
zumpaaahh ‘ane zuzur,
maybe 288 triangles
I think their are 90000 tringle in this pic i count it if u have porwer please u can also count it and let me know
thankx
My name is Kumail Ok
56 triangles..
upss.. i found 64 triangles for the last
4
ABOUT 24
64. (n+1)to the 3
there are 8 triangles
29
YES!!!!!! ILY!!!!!!!!!!
I think there are 64 triangles < who else does because i'm not american and i'm not dum!!!!!!!!!!!!!!!!!
8
The answers is 64 triangle
I counted 76 triangles.
there are only 10. others are not triangles dont make it hard folks its so simple. there are only ten, dont count the entire triangle repeatedly.
Ohkay, here’s the deal….. YOU ARE ALL RETARDED!!!!!!!!!!! There are clearly 29 triangle… i don’t see why we are all fighting oer how many triangles there are…. I think that it is impossible to have 60 or 64 triangles…… You are all stupid….. Btw I’m 15….. hahahhaha
80
ini yang bener berapa jawabannya?
the right answer is 62 triangle
84
I found it 16 triangles at the first time, but I believe that the correct answer is 64. I’m still counting.
36×2+4
i found 80
i really wanna know the correct answer >_<
72
I think 64 is the right answer!! Please tell me the answer cos I really wanna know
soo what is the right answer? ^_^
80
whoever said 76, we are on the same page..yeeha..
equation:
(4*10*2)-4 = 76
the first 4 means there is 4 “big” triangle,
then there is 10 “small” triangle each,
2 means reflecting right and left
-4 means substracting the duplication (4 triangle in the middle).
Yeah I know…only me who can understand what im talkin bout..
im got a 19
I got 76 too. But i solved it in a different way.big ones are 16*2 = 32 – 4 because big triangles are repeated = 28. Small by 1’s triangles = 12*2 = 24. Small by 2’s triangles is 8*2 = 16 then small by 3’s triangle is 4*2= 8 28+24+16+8 = 76 🙂
i got 76
I have 64.. Maybe you count tetrahedrons, or counting something two times?
I got 58…
I’m Indonesian, so I could wrong…
LOL
64..!! 🙂
Yes, 64 🙂
(10*4*2)-(4*4) = 64
But… I’m from Ukraine =)
It’s 64.
52 ?
I’ve got 76 as well and I’m indonesian 🙂
64 count 1 by 1 🙂
64
12X2= 24
4X2=8
4X2=8
4X3=12
4
=64
I see one triangle with a lot of unimportant lines in it.
I only got 10
Triangles = 6x4x2 + 16 = 64.
15
10
64! And I’m Indonesian. Could I live in USA? 😀
66
8
26
64
14 numnuts you guys are counting rhomuses too if you see 64 or any number over 14 for that matter.
there are only 26 triangles…one large one, one small and the rest are little broken down into a square type that u must devide to see the triangles…
49 dude…. (I’m indonesian..)
There is only one!!!
48
I believe that 56 is the correct answer, but it’s tricky enough that I might have missed some. I think that these guys owe us an answer.
64
61 …… indonesian
Damn…its 64
I onlt got 74 🙁
-Philippines
6
I see 8…
28
(8*10) – 10 = 70
Got 76 then googled it. Photobucket has a pic confirming 64 that the last figure should say 4•3•2. Thoughts?
I counted 198. Let’s start by following the lowest line going up to the right. There are 4 segmented triangles, but combined into double segments, there are 3 more. Combined into triple segments, there are two. And combined as a quadruple segment, there’s 1. So 4+3+2+=10 now there are four segments like that separated by lines going up to the right. So it’s 40+30+20+10=100. Now repeat for the other side. 100+100 = 200. This number accounts for 2 instances of the largest internal triangle at the base and the triangle comprised of the entierty of the shape. Subtract one of each instance. 200-2=198.
So this is over a year old and people are still posting. what’s the answer?
i found 74 .. [bangladeshi]
You’re all blind… first, there’s no mathematic equation that applies, because permutations don’t exist at all three points, so you can throw that one right out the window. If you simply use your eyes and your brain, it’s simple to come up with the right answer which is 40… no more, no less…
There are 14 triangles!!
can any 1 tell me the ri8 answer
There are 74.
64! Use your eyes.. Lol 16 off the main base and 48 little ones coming out of the corners…
intially i got 76, but dan again i got 79 again. Am frm somalia
its 79, am da genious frm somalia
My 6th grade math class got 60!! We counted the triangles in the A’s and the word triangle! =)
Only One triangle, the other triangles are its friends….
76 Triangles
-People’s Republic of China
16×2-1 + 12×2-(2×2-1) + 8×2 – 3×2 + 1 = 63
Yeah, the answer is 64.
– Start from bottom left corner, top (or first) column. In that column alone you can make four different triangles (corner to first “cross” line, corner to second “cross” line…).
– Repeat for the other columns. You should get 16.
– Now we make wider triangles out of TWO columns, still from the bottom left corner. You can find 12 more this way.
– Do the same thing with three columns (8 more) and four columns (4 more).
– We now have 40 triangles. We can repeat the same process from the right, but we CANNOT count triangles that touch the left corner (basically we can’t use the bottom column), as we have counted them already. You should get 24 more, a total of 64.
i found 75
Go out and get girlfriends. Stop sitting around doing puzzles like this.
I got 12, some of them r quadrilaterals 😛
there are 12
There are at least 50
ATLEAST 16
64 triangles are in given figure..
Nop guys, there are 72 triangles in this picture, pretty sure of myself 🙂
there are only 35 im a mathemitician expert
64
42
I got 64
2(4×4+4×3+4×2+4×1)-(4×4)=64
There’s a triangle in every upper case A. 🙂
7
A triangle has only three sides