# how does this triangle puzzle work? **URL:** \ **Category:** Factual Questions\ **Created:** [August 13, 2003, 7:22pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987 "2003-08-13T19:22:01Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Hampshire](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hampshire/32/4887_2.png) [@Hampshire](https://boards.straightdope.com/u/Hampshire)\ **Post date:** [August 13, 2003, 7:22pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/1 "2003-08-13T19:22:01Z")
I’ve tried analyzing this and can’t figure it out: [http://www.simeonmagic.com/triangle/triangle1.htm](http://www.simeonmagic.com/triangle/triangle1.htm) (sorry, I don’t know how to link) The triangle on a whole is 32.5 units squared. One of the internal trinagles is 5 units squared and the other is 12 units squared. So why does the remaining square equal either 15 or 16 units squared depending on where the internal triangles are placed. Adding the sum of the parts one way equals 32 and the other 33. Why do the sum of the parts not equal 32.5?? ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [August 13, 2003, 7:28pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/2 "2003-08-13T19:28:36Z")
There have been many threads about this. The lines are not perfectly straight, the figure is not drawn perfectly accurate (depending which version you look at), it’s off just enough to account for the difference. ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [August 13, 2003, 7:32pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/3 "2003-08-13T19:32:02Z")
This has come up quite a few times. Here’s just one: [http://boards.straightdope.com/sdmb/showthread.php?threadid=89065](http://boards.straightdope.com/sdmb/showthread.php?threadid=89065) ---
**Author:** ![shelbo](https://avatars.discourse-cdn.com/v4/letter/s/3d9bf3/32.png) [@shelbo](https://boards.straightdope.com/u/shelbo)\ **Post date:** [August 13, 2003, 8:16pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/4 "2003-08-13T20:16:00Z")
The best answer from the other thread: > [@](#): > > by **friedo** > Too expand on hajario (and, BTW, I got this wrong in one of the old threads) all you need to do is calculate the slope of the (apparently) similar triangles. You will see they are not similar. > > Red traingle = 8 over by 3 up. Slope = 8/3 = 2.666… > > Green triangle = 5 over, 2 up. Slope = 5/2 = 2.5. > > Thus the “big” triangle is not a triangle at all. The two portions have very slightly different slopes. You are dealing with a four-sided figure. Actually, you are dealing with 1 four sided figure, and one 8 sided figure! ---
**Author:** ![Hobie\_the\_One](https://avatars.discourse-cdn.com/v4/letter/h/e99b99/32.png) [@Hobie\_the\_One](https://boards.straightdope.com/u/Hobie_the_One)\ **Post date:** [August 14, 2003, 2:51pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/5 "2003-08-14T14:51:02Z")
Sorry, but I have to nitpick. The slopes are actually Red Triangle = 3 up by 8 over. Slope = 3/8 = .375 Green Triangle = 2 up by 5 over. Slope = 2/5 = .4 They **are** still different. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 14, 2003, 3:25pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/6 "2003-08-14T15:25:05Z")
Did you know that the missing square costs exactly a dollar and sounds like a duck? ---
**Author:** ![nocturnal\_tick](https://avatars.discourse-cdn.com/v4/letter/n/3d9bf3/32.png) [@nocturnal\_tick](https://boards.straightdope.com/u/nocturnal_tick)\ **Post date:** [August 14, 2003, 6:09pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/7 "2003-08-14T18:09:13Z")
duck? ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [August 14, 2003, 6:14pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/8 "2003-08-14T18:14:10Z")
“Quack!” \ " … !" \ ---
**Author:** ![tanstaafl](https://avatars.discourse-cdn.com/v4/letter/t/ba8739/32.png) [@tanstaafl](https://boards.straightdope.com/u/tanstaafl)\ **Post date:** [August 14, 2003, 6:50pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/9 "2003-08-14T18:50:02Z")
Is there an echo in here? 😉 ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 14, 2003, 7:58pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/10 "2003-08-14T19:58:32Z")
Furthermore, it smells of cat food and is the only square that cannot jump. ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [August 14, 2003, 8:03pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/11 "2003-08-14T20:03:48Z")
Hungry though I may be for knowledge, squares like this make me so angry and … and … I dunno: Something else. ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [August 14, 2003, 9:23pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/12 "2003-08-14T21:23:36Z")
> [@](#): > > \*Originally posted by MonkeyMensch \* > \*\*Hungry though I may be for knowledge, squares like this make me so angry and … and … I dunno: Something else. \*\* Brilliant… Absolutely brilliant! ::applause:: ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [August 14, 2003, 9:46pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/13 "2003-08-14T21:46:49Z")
Yeah, but where did the missing leprechaun go? ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 14, 2003, 9:51pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/14 "2003-08-14T21:51:18Z")
My friend has a square that he is worried might be smaller than average; what is the average size of a sqare? ---
**Author:** ![AndrewL](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@AndrewL](https://boards.straightdope.com/u/AndrewL)\ **Post date:** [August 14, 2003, 9:56pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/15 "2003-08-14T21:56:51Z")
Is the missing square large enough to hide the third -gry in? ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 14, 2003, 10:08pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/16 "2003-08-14T22:08:27Z")
All your square are belong to us. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [August 14, 2003, 10:10pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/17 "2003-08-14T22:10:16Z")
When come back, bring square! ---
**Author:** ![UncleBill](https://avatars.discourse-cdn.com/v4/letter/u/d26b3c/32.png) [@UncleBill](https://boards.straightdope.com/u/UncleBill)\ **Post date:** [August 14, 2003, 11:14pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/18 "2003-08-14T23:14:38Z")
1. This is just an optical illusion wherein the brain “fills in the blanks” and makes you see what truly is not there. 2. A simple analytical look matching the intersections of the triangle legs to the background grid will reveal this. 3. Hi Square! ---
**Author:** ![whatami](https://avatars.discourse-cdn.com/v4/letter/w/85f322/32.png) [@whatami](https://boards.straightdope.com/u/whatami)\ **Post date:** [August 14, 2003, 11:57pm UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/19 "2003-08-14T23:57:23Z")
> [@](#): > > \*Originally posted by Mangetout \* > \*\*My friend has a square that he is worried might be smaller than average; what is the average size of a sqare? \*\* Be honest, does the size of the square really matter? ---
**Author:** ![MonkeyMensch](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@MonkeyMensch](https://boards.straightdope.com/u/MonkeyMensch)\ **Post date:** [August 15, 2003, 12:08am UTC](https://boards.straightdope.com/t/how-does-this-triangle-puzzle-work/194987/20 "2003-08-15T00:08:46Z")
This is actually an old mathematical debate. The area of the triangle is actually 32.4999~. The difference between this value and the genuine value of exactly 32.5 is represented by the square seen in the bottom figure. I hope this helps…