IQ test. WARNING—not suitable for theists—Cognition Required...
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15-12-2016, 07:31 AM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
I found exactly 24. I was surprised when I found out that this was the solution; the way you phrased it made it sound like it was going to be a lot more than 20.

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15-12-2016, 08:28 AM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(14-12-2016 09:19 PM)Aliza Wrote:  
(14-12-2016 09:08 PM)SYZ Wrote:  Another IQ-type test...

It's claimed that if you can discern 20 triangles (in all/any configurations) in this diagram, you have an IQ of at least 120 or "superior" as per WAIS–IV, WPPSI–IV, and Stanford–Binet fifth edition.

[Image: CzGsFh7XUAIM2r1.jpg]

The actual number of triangles comes as a surprise, and I'm guessing few people will get the right number. I didn't. Ouch!

The answer, with explanatory diagrams is here...

[Image: CzUulE7XAAA9aEy.jpg]

Huh

I made it to 20 triangles with ease. My actual tested IQ is respectably higher than 120. How do you explain that? Dodgy

Ditto, though lost track after 22 and had to check the answers.

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15-12-2016, 08:42 AM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(15-12-2016 08:28 AM)Shai Hulud Wrote:  
(14-12-2016 09:19 PM)Aliza Wrote:  I made it to 20 triangles with ease. My actual tested IQ is respectably higher than 120. How do you explain that? Dodgy

Ditto, though lost track after 22 and had to check the answers.

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15-12-2016, 09:36 AM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
I got 23, but I can't for the life of me figure out which one I missed. When looking at the answer, I seem to recall finding each of the 24. Blink

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15-12-2016, 09:37 AM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
I think finding a way to approach it systematically to facilitate keeping track of the ones you've already found and to know when you've covered every possibility is key to this problem. In fact certainty that I have them all and have not double counted any eluded me. Maybe with more work I could achieve that certainty but I can tell it won't be easy. But if Syz knows of an official/sanctioned answer to how many are possible I would rather just be told. Big Grin

As a former math teacher I enjoy the challenge of counting problems. Since I stupidly laid out my solutions without spoiler tags at first, I can offer a another good but different triangle counting problem. It is a better problem if you don't know the number of possible solutions ahead of time, but here it is for those who either want the hint or for checking when you think you have them all.

14


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.

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15-12-2016, 04:58 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(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.

- 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.

- 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 ◢◩.

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15-12-2016, 05:10 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(14-12-2016 09:19 PM)Aliza Wrote:  
(14-12-2016 09:08 PM)SYZ Wrote:  Another IQ-type test...

It's claimed that if you can discern 20 triangles (in all/any configurations) in this diagram, you have an IQ of at least 120 or "superior" as per WAIS–IV, WPPSI–IV, and Stanford–Binet fifth edition.

[Image: CzGsFh7XUAIM2r1.jpg]

The actual number of triangles comes as a surprise, and I'm guessing few people will get the right number. I didn't. Ouch!

The answer, with explanatory diagrams is here...

[Image: CzUulE7XAAA9aEy.jpg]

Huh

I made it to 20 triangles with ease. My actual tested IQ is respectably higher than 120. How do you explain that? Dodgy

Shhhh Aliza, new atheists can't fathom that a person can be intelligent and still believe in a god.
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15-12-2016, 05:45 PM (This post was last modified: 15-12-2016 05:49 PM by Full Circle.)
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
I took me 5 minutes but I counted 20 then I checked and saw there were 24... crap.

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15-12-2016, 06:05 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(15-12-2016 05:45 PM)Full Circle Wrote:  I took me 5 minutes but I counted 20 then I checked and saw there were 24... crap.

Hey the requirement was only 20.
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15-12-2016, 07:53 PM
RE: IQ test. WARNING—not suitable for theists—Cognition Required...
(15-12-2016 09:37 AM)whateverist Wrote:  I think finding a way to approach it systematically to facilitate keeping track of the ones you've already found and to know when you've covered every possibility is key to this problem. In fact certainty that I have them all and have not double counted any eluded me. Maybe with more work I could achieve that certainty but I can tell it won't be easy. But if Syz knows of an official/sanctioned answer to how many are possible I would rather just be told. Big Grin

As a former math teacher I enjoy the challenge of counting problems. Since I stupidly laid out my solutions without spoiler tags at first, I can offer a another good but different triangle counting problem. It is a better problem if you don't know the number of possible solutions ahead of time, but here it is for those who either want the hint or for checking when you think you have them all.

14


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.

I have done the OP triangle problem before, so I'm not going to address that. I'll go treat your problem off line when I have some time. I had some spare time about 20 YA, and looked into how many distinct configurations of cubes one could assemble for a given number of cubes. I got up to 7 cubes before life caught up with me, and I haven't got back to it yet. I'm thinking that a person could come up with a formula, but haven't got that far. It's on my list of things to do, but probably about #10 in line. I think that I also lost the file that had all the pictures. Sadcryface That was a lot of work.
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