IQ test. WARNING—not suitable for theists—Cognition Required...
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15-12-2016, 08:01 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
Sorry about that. It didn't immediately occur to me but I don't know any way to actually show the shapes formed via the computer. So not a good problem.

(15-12-2016 04:58 PM)Paleophyte Wrote:  
(15-12-2016 09:37 AM)whateverist Wrote:  Another Triangle Problem: How many distinctly different**** shapes can you make by connect four congruent (i.e., same sized) isosceles right triangles* in such a way that one solid figure*** is formed and that each triangle is connected to other triangles only along whole sides only**?

*An isosceles, right triangle is what you get if you divide a square in half across a diagonal. (The two sides of the triangle formed which had been sides of the square will be equal, making it isosceles, and the angle between them -coming from the square- must be 90 degrees, making it a right triangle as well.)

**If you allowed triangles to be connected by half a side, or a third, fourth, etc. there would be an infinite number of shapes possible. No fun for counting.

***The solid figure requirement is to rule out shapes consisting of two solid regions connecting only by a point. For example, if you used the four triangles to make two squares and then connected the two squares only by a corner, you would have two solid shapes, not one. That isn't allowed.

****Finally, what counts as distinctly different? If you come up with two shapes where one would exactly overlay the other either by rotating or flipping it, then it does not count as a separate, distinctly different shape for this problem.

Note: this is a plane geometry problem. All the triangles must lie in the same plane.

Needs clarification:

- Is overlap permitted?
Four isosceles triangles stacked atop one another in the same plane are all "joined along whole sides only" and result in one original isosceles triangle.

Good point. No, no overlap is permitted.


(15-12-2016 04:58 PM)Paleophyte Wrote:  - Does "distinctly different" rule out two objects of identical geometry but different sizes?
Are the squares made using two and four triangles considered identical? Moot if you can't use overlap.

Not sure I understand your question here (especially the part I bolded and took out of spoiler tags). Since no overlap is allowed, the total area of each figure formed must be the same since the four triangles are all congruent.


(15-12-2016 04:58 PM)Paleophyte Wrote:  - Does "distinctly different" rule out two objects of identical geometry and size but different internal joins of the triangles?
◢◩ and ◥◩ cannot be rotated or flipped to be identical if you count the internal join between the black and white triangles in the square. Flipping ◥◩ gets you ◪◣ which is not the same as ◢◩.

No, the markings/outline of the four triangles which go into forming each figure make no difference to its being distinctly different. The only criteria is whether one of the figures formed would exactly fit over another; if it would, they do not count as different and you could only count one of them.

I'm afraid this problem doesn't lend itself well to an online forum afterall.

“Tiger got to hunt, bird got to fly;
Man got to sit and wonder 'why, why, why?'
Tiger got to sleep, bird got to land;
Man got to tell himself he understand.”

― Kurt Vonnegut, Cat's Cradle
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16-12-2016, 03:27 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
What is this????

I can't comprehend!!!!

What are these shapes and symbols???

*dies*

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16-12-2016, 03:31 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(16-12-2016 03:27 PM)kingschosen Wrote:  What is this????

I can't comprehend!!!!

What are these shapes and symbols???

*dies*

There there. We *did* warn you, right in the thread title. But then, I guess your reading comprehension might not be so great either.

Consider Maybe I should rewrite this post with shorter words.




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(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
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16-12-2016, 03:52 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(16-12-2016 03:27 PM)kingschosen Wrote:  What is this????

I can't comprehend!!!!

What are these shapes and symbols???

*dies*

Shapes are hard for people like us. Huh
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17-12-2016, 12:08 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(16-12-2016 03:52 PM)Aliza Wrote:  Shapes are hard for people like us.

Not for us Aussies...

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—all too easy in fact. Big Grin

I'm a creationist... I believe that man created God.
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17-12-2016, 03:47 PM
IQ test. WARNING—not suitable for theists—Cognition Required...
(14-12-2016 09:26 PM)jennybee Wrote:  I found 20 triangles. What do I win?


This pretty picture of a bee on a flower.
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17-12-2016, 06:19 PM (This post was last modified: 17-12-2016 06:23 PM by Leerob.)
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
oh wow sweet. I love these things. I also got 24. I am not sure if that is a good or bad sign. Maybe there are even more triangles? I didn't find more though

"Freedom is the freedom to say that 2+2=4" - George Orwell (in 1984)
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17-12-2016, 07:57 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(17-12-2016 06:19 PM)Leela Wrote:  oh wow sweet. I love these things. I also got 24. I am not sure if that is a good or bad sign. Maybe there are even more triangles? I didn't find more though

24 appears to be the consensus reality result. I don't see any more than that, either, though.
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