26 Feb Posted by Sergey Page » 184 Comments »
How Many Triangles Are There in This Picture? | 92.6% of Americans Get This Question Wrong [PIC]
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92.6% of Americans Get This Question Wrong
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92.6% of Americans Get This Question Wrong
GiveUpInternet.com Forum Posts
There's 184 Comments So Far
February 28th, 2009 at 3:38 pm
8
February 28th, 2009 at 7:48 pm
I got 44
March 1st, 2009 at 10:23 pm
i got 53 trangles
March 1st, 2009 at 11:38 pm
23??
March 1st, 2009 at 11:39 pm
now i got 16 =_=
March 2nd, 2009 at 6:33 am
in the triangle, there are little ones….then the the littler ones form bigger ones people…so easy
March 2nd, 2009 at 2:30 pm
Nate, the question is “how many”, not “is it hard?”
March 2nd, 2009 at 3:11 pm
there are 9
March 2nd, 2009 at 5:26 pm
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*~
March 2nd, 2009 at 6:43 pm
68.
You forgot the triangles going up the middle PWNAGE.
March 3rd, 2009 at 1:52 am
Actually, I’m wrong.
It’s 65.
March 4th, 2009 at 2:14 am
I counted twice and got 70 both times. I’m quite sure of it, but is there any definite answer to be found?
March 4th, 2009 at 2:23 am
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.
March 4th, 2009 at 7:46 pm
i count 23? im such a loser boo hoo lolz
March 5th, 2009 at 7:44 am
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…
March 6th, 2009 at 9:08 pm
I got 30……
March 7th, 2009 at 7:57 am
38
March 13th, 2009 at 12:02 am
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…
March 15th, 2009 at 8:34 pm
there are 9
March 17th, 2009 at 5:48 pm
86
March 18th, 2009 at 3:53 pm
I get 10. *shrugs*
March 18th, 2009 at 4:00 pm
Actually, I missed a few. I change my answer to 52. Sorry.
March 18th, 2009 at 9:35 pm
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.
March 20th, 2009 at 1:21 pm
it’s 64 ^^
March 20th, 2009 at 6:26 pm
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.
March 22nd, 2009 at 8:04 pm
25
March 23rd, 2009 at 6:16 pm
i got like 28
March 23rd, 2009 at 9:33 pm
hmmmm, 76 here
March 24th, 2009 at 5:29 pm
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.
March 24th, 2009 at 9:52 pm
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.
March 29th, 2009 at 8:01 pm
14?
March 31st, 2009 at 2:15 pm
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.
March 31st, 2009 at 8:06 pm
theres 1
April 3rd, 2009 at 6:08 pm
17???
April 4th, 2009 at 4:43 pm
52
April 5th, 2009 at 2:37 pm
15
April 11th, 2009 at 6:18 pm
26 triangles
April 11th, 2009 at 6:20 pm
49 triangles now
April 11th, 2009 at 6:21 pm
51 now
April 11th, 2009 at 7:10 pm
i think 8 or 24 i am 11 and still smarter than all yall 8^)
April 11th, 2009 at 7:17 pm
by the way im correct i gradguated like most of you didnt you guys dont know how to count
April 12th, 2009 at 6:57 am
any one there
April 12th, 2009 at 7:03 am
there r 32
April 12th, 2009 at 5:08 pm
i think there are 8….DUH!!!
April 16th, 2009 at 11:59 am
41 u all r retarded
April 16th, 2009 at 12:05 pm
40 u all r not math professers
s l
April 21st, 2009 at 7:49 pm
faggots it’s 200
April 22nd, 2009 at 5:48 pm
No. It’s definitely 64. I did the math, not using PWNAGE’s formula though. Just found a pretty simple pattern.
April 28th, 2009 at 6:00 pm
It’s definitely 64 u guys, and solsta… ur an idiot.
May 3rd, 2009 at 11:28 am
You guys are i___s. Triangles have 3 SIDES. How many shapes have 3 sides up there?
There are 8 triangles in the picture.
May 5th, 2009 at 9:09 pm
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
May 6th, 2009 at 12:36 am
I counted 50 since Every 3 sided object that can be created in this design is a triangle, there may even be more, LOL.
May 9th, 2009 at 6:51 am
30
May 12th, 2009 at 7:28 pm
it is clearly 74, im in a math academy, i can count
May 14th, 2009 at 9:43 pm
what the hell triangles only have 3 sides
its 8
May 15th, 2009 at 4:05 pm
79, so whats the point of not supplying the answer?
May 18th, 2009 at 11:08 pm
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
May 22nd, 2009 at 2:45 pm
74
May 24th, 2009 at 5:28 am
125
May 26th, 2009 at 7:42 pm
there’s def. 16
May 26th, 2009 at 7:50 pm
srry theres 54
May 26th, 2009 at 7:53 pm
now there’s 56
final answer let me know if anybody else gets 56
May 26th, 2009 at 8:03 pm
there are 77 srry 4 changing my answer so much this time i double scratch that triple checked
May 27th, 2009 at 7:46 pm
64. final answer.
May 29th, 2009 at 2:19 am
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
May 29th, 2009 at 2:09 pm
23
May 31st, 2009 at 8:07 pm
theres ONE. always making things harder than they should be.
June 5th, 2009 at 5:55 pm
57
June 7th, 2009 at 10:10 am
First count I get 70
June 7th, 2009 at 10:38 am
44
June 7th, 2009 at 6:51 pm
They’d be (10-4)x4x2+(4)x4x1=64 different triangles. Greeting from Sapienza:Università di Roma.
June 7th, 2009 at 8:56 pm
It’s 8 the others are a dimond of some sort
June 9th, 2009 at 12:05 pm
so quit counting them with the triangles
June 10th, 2009 at 11:15 am
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.
June 10th, 2009 at 11:21 am
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.
June 11th, 2009 at 6:42 am
16, defenitely.. Who knows the correct answer??
June 11th, 2009 at 3:38 pm
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!
June 12th, 2009 at 8:16 am
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.
June 12th, 2009 at 8:23 am
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?
June 12th, 2009 at 7:06 pm
Solution: 64
http://www.iwpcug.org/davidbro/puz0603.htm
June 12th, 2009 at 8:54 pm
I counted 27 triangles
June 12th, 2009 at 8:58 pm
oops counted again and there are definitely 32 triangles
June 12th, 2009 at 8:59 pm
ahh okay i found 2 more my FINAL answer is 34 triangles that is THE answer
June 12th, 2009 at 9:00 pm
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.
June 14th, 2009 at 6:10 am
31
June 14th, 2009 at 12:29 pm
64
June 14th, 2009 at 3:38 pm
76
June 14th, 2009 at 3:42 pm
oops! i counted the 9 small quads. sorry, it’s 64
June 15th, 2009 at 9:42 pm
I counted 12
June 15th, 2009 at 10:31 pm
68 triangles.
June 15th, 2009 at 10:35 pm
i counted way off there are 64
June 21st, 2009 at 4:52 am
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)
June 22nd, 2009 at 10:44 pm
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)
June 23rd, 2009 at 7:08 am
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
June 25th, 2009 at 2:03 pm
64 I know it is right!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
June 27th, 2009 at 10:57 pm
i say 8
July 6th, 2009 at 9:19 pm
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!
July 10th, 2009 at 10:00 am
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.
July 12th, 2009 at 3:24 am
Jarjar… You’re an i_i_t… Did you (does anyone) read any previous posts?
July 12th, 2009 at 8:17 pm
27
July 14th, 2009 at 12:13 pm
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!
July 20th, 2009 at 3:47 pm
The answer is 19
July 20th, 2009 at 9:22 pm
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?
July 20th, 2009 at 9:24 pm
acually 10 3 sided figures
July 24th, 2009 at 10:11 am
its either 12342153 or 9
July 25th, 2009 at 10:10 am
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?
July 25th, 2009 at 10:11 am
I saw now It is 64
maybe i will find more
July 25th, 2009 at 10:16 am
I’ve just read comments, it’s not 64 at all I counted 86 and maybe it will be more
July 27th, 2009 at 4:19 pm
hey guys this may seem strange but i got 87 in my counting. no math just counting
July 31st, 2009 at 5:43 pm
I got 72
August 1st, 2009 at 6:40 pm
I got 26
August 5th, 2009 at 12:40 pm
its 64
August 5th, 2009 at 5:52 pm
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!!!!
August 7th, 2009 at 7:10 am
Surely its 10 including the main triangle they are all inside!
There’s only diamonds in the upper half !
August 7th, 2009 at 7:11 am
Or actually 12
August 7th, 2009 at 7:13 am
or actually loads of them …aahhh loads and loads !!
August 9th, 2009 at 3:09 am
58
August 12th, 2009 at 2:04 pm
I counted 8, then 10, then like 20-something, now 50.
I am almost 100% sure there are only 50.
August 12th, 2009 at 2:06 pm
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.
August 12th, 2009 at 2:08 pm
Ahhhhhh nevermind I see the rest of them now… Crap hold on.
August 12th, 2009 at 2:08 pm
I was wrong
64 triangles.
August 14th, 2009 at 4:09 am
you guys are stupid its 64
August 14th, 2009 at 4:10 am
you cant split the diamonds in half….
August 19th, 2009 at 5:37 pm
i got 41.
i cant find anymore than that.
so how are you getting 64?
August 25th, 2009 at 12:41 am
Its 763 IDIOTS.
BTW.
“Im from Harvard University”
-Notice the tinge of Sarcasm?
September 3rd, 2009 at 9:14 pm
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
September 16th, 2009 at 2:43 pm
its got to be 64, and how are you idiots getting 8, why dont you try thinking outside the box for a change
September 18th, 2009 at 3:06 am
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.
September 18th, 2009 at 3:10 am
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. =]
September 18th, 2009 at 3:15 am
oh wait… then i say 10.. coz the big one has lines through it&&im sticking to my lazy theory… =]
October 16th, 2009 at 8:14 pm
a lot.
October 19th, 2009 at 10:53 pm
69
October 21st, 2009 at 1:15 pm
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.)
October 22nd, 2009 at 8:03 pm
there are 10 TRIANGLES
October 22nd, 2009 at 8:05 pm
never mind im a retard maybe there is 27.. I DONT KNOW
October 25th, 2009 at 11:08 am
http://www.iwpcug.org/davidbro/puz0603.htm
October 28th, 2009 at 11:44 pm
its 68 you guys are all missing the middle triangles including the one that forms it all
November 11th, 2009 at 7:22 pm
I guess 67, but I lost count at 47, and kept on counting, this was a great way to waist 5mins.
November 17th, 2009 at 8:22 am
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.
November 24th, 2009 at 5:39 am
16
January 10th, 2010 at 12:40 pm
igot 11
January 16th, 2010 at 9:08 am
OMG!How its could be 64?you do not think the general image and the bottom. one word – the Americans. So there are 66
January 16th, 2010 at 9:09 am
Stop.70 now O_O
January 16th, 2010 at 9:16 am
Ok.I’m serious now.and recent decision is 78.
January 31st, 2010 at 1:39 pm
The answer is 64.
February 6th, 2010 at 1:57 am
(n+1)^3, n= number of lines in the triangle = 3
(3+1)^3
4^3=64
February 7th, 2010 at 3:04 am
50
February 7th, 2010 at 3:08 am
whoops, i meant 64
February 7th, 2010 at 6:59 am
its 30 i m sure
February 24th, 2010 at 8:59 pm
It is 30. =) and i am not a genius=)
March 12th, 2010 at 6:11 pm
From South Africa the answer is 64
April 11th, 2010 at 12:50 pm
im no genius but i count 8
April 12th, 2010 at 5:02 am
Its way more than 8!!!
April 12th, 2010 at 8:22 am
I counted 8 but I think there are more some way or another
April 12th, 2010 at 8:24 am
no i change my mind there are 20
April 12th, 2010 at 2:04 pm
There is only one triangle.
April 23rd, 2010 at 2:41 pm
i count 52, might have missed some.
April 23rd, 2010 at 5:41 pm
There’s 8 and you have to believe me cause I’m Albert Einstein.
April 25th, 2010 at 11:47 am
64.
April 28th, 2010 at 5:45 pm
yea i counted 64
May 13th, 2010 at 7:20 am
pretty sure its 68 could be more
May 18th, 2010 at 6:32 am
I found 64. hmm.
May 18th, 2010 at 12:03 pm
i am a genius there are 8
May 18th, 2010 at 6:07 pm
i counted 39… or maybe 40 im not counting again!
June 18th, 2010 at 2:41 pm
I counted 10 triangles
July 3rd, 2010 at 11:25 am
i counted 30 i have no idea were i got dat xxx <3
July 7th, 2010 at 11:30 am
no chance 64 theres about 21 dur brains
July 15th, 2010 at 2:37 pm
76
July 16th, 2010 at 1:46 pm
13
July 16th, 2010 at 4:20 pm
I counted 58 but i belive that there is more triangles.
July 19th, 2010 at 10:48 pm
theres 1 triangle
July 19th, 2010 at 10:48 pm
nevermind theres 3 if u can see it
July 20th, 2010 at 2:46 pm
11…
July 21st, 2010 at 4:48 pm
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.
July 21st, 2010 at 5:10 pm
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.
July 30th, 2010 at 12:22 pm
i say 8
August 12th, 2010 at 2:27 am
i count 8
August 18th, 2010 at 11:07 am
the solution is here:
http://www.iwpcug.org/davidbro/puz0603.htm
(64)
August 23rd, 2010 at 2:18 pm
i think theres about 30/40 i keep losing track ! <333 xxxx
August 28th, 2010 at 10:42 am
12??
September 1st, 2010 at 9:28 am
21
September 2nd, 2010 at 8:22 am
67;D
September 5th, 2010 at 5:57 am
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.
September 7th, 2010 at 12:44 am
8 because other dont have 3 sides 0-0
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