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        riddles >> hard >> Nonverbal IQ Test (Other Half of Ultra Test)
        
(Message started by: Polymath101 on Apr 1st, 2009, 6:14pm)
Title: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Polymath101 on Apr 1st, 2009, 6:14pm
37. If the four sides of a square consist of rods each of which is painted white or black, six distinct color patterns are possible: (1) all sides white, (2) all sides black, (3) one side white and the rest black, (4) one side black and the rest white, (5) two adjacent sides white and the other sides black, and (6) two opposite sides white and the other sides black. Suppose that each of the twelve edges of a cube is a rod that is painted white or black. How many distinct patterns are possible if any three of the rods are painted white and the other nine are painted black?

38. Suppose that the figure at right consists of nine rods of equal length joined together to form four equilateral triangles of equal size. If two of the rods are painted white and the remaining seven rods are painted black, how many distinct patterns can thereby be created?

39. Suppose an octahedron consists of twelve rods all of equal length and forming eight equilateral triangles -- the eight sides of the octahedron. If any two of the rods are painted white and the rest black, how many distinct patterns are possible?

40. Suppose that the figure at right consists of thirty rods of equal length that form twelve pentagonal figures of equal size, which form the twelve sides of a regular dodecahedron. If any two rods are painted white and the remaining twenty-eight are painted black, how many distinct patterns are possible?

41. Suppose an octahedron consists of twelve rods all of equal length and forming eight equilateral triangles -- the eight sides of the octahedron. If any three of the rods are painted white and the rest black, how many distinct patterns are possible?

42. If lightbulbs are put at two different corners of a square, two distinct patterns are possible: one in which the bulbs are at opposite ends of any side of the square, and one in which the bulbs are diagonally across from one another. If lightbulbs are put at four different corners of a cube, how many distinct patterns are possible?

43. If lightbulbs are placed at two different vertices of a regular dodecahedron, how many distinct patterns are possible?

44. Suppose that lightbulbs are placed at any three distinct vertices of a regular icosahedron (illustrated at right). How many distinct patterns can thereby be formed?


Draw the figure that should fill the blank (identified by the question mark) in each of the following series:

For the problems that require images i have provided the following link:

http://www.eskimo.com/~miyaguch/ultra.html

Show your steps!
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by rmsgrey on Apr 2nd, 2009, 4:27pm
For #37, I get [hide]...9..[/hide] distinct patterns.

#38: [hide]...8..[/hide] distinct patterns.

I might come back to the rest later...
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Hippo on Apr 4th, 2009, 12:09am
This belong to medium, or may be easy.
At least the top part I have read.
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Polymath101 on Apr 15th, 2009, 7:50pm

on 04/02/09 at 16:27:04, rmsgrey wrote:
For #37, I get [hide]...9..[/hide] distinct patterns.

#38: [hide]...8..[/hide] distinct patterns.

I might come back to the rest later...


If you could show me the steps to how you arrived at your answers, I would greatly appreciate it! Also, come back to the rest of the problems please! You seem to be a very intelligent person!
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Polymath101 on Apr 15th, 2009, 7:51pm

on 04/04/09 at 00:09:35, Hippo wrote:
This belong to medium, or may be easy.
At least the top part I have read.


If this is so easy, why haven't you posted any answers? ;D
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by rmsgrey on Apr 16th, 2009, 6:24am

on 04/15/09 at 19:50:23, Polymath101 wrote:
If you could show me the steps to how you arrived at your answers, I would greatly appreciate it! Also, come back to the rest of the problems please! You seem to be a very intelligent person!

It's just a matter of methodically listing all the possibilities.

For example, with the triangle, the obvious distinction is between inner and outer rods.

There's only one pattern with two white inner rods.

If the first white rod is outer, then all 6 possible locations are equivalent. If the other rod is inner, that gives three possibilities (forming a 60 degree angle, a 120 degree angle, or parallel and not touching).

If the other rod is outer, then they can both be at the same end of their sides of the triangle (clockwise or counter-clockwise) which only offers one pattern, or at opposite ends, in which case they can be sharing a corner, sharing an edge, or not touching, for three more patterns.

So, putting it all together, that's eight patterns.


For the cube, with three white edges, it's a little trickier because it's in three dimensions rather than two, but a little simpler because of the increased symmetry. A good place to start is by looking at three connected, two connected and an odd one, and all three disconnected.
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Grimbal on Apr 16th, 2009, 6:40am
One problem with the cube is that it is not specified whether mirror images are considered equal or not.
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by rmsgrey on Apr 17th, 2009, 5:41am

on 04/16/09 at 06:40:46, Grimbal wrote:
One problem with the cube is that it is not specified whether mirror images are considered equal or not.


Good point - my answer counted reflections as the same pattern - if you count them as distinct, then the four asymmetric patterns in my count need to be counted twice.
Title: Re: Nonverbal IQ Test (Other Half of Ultra Test)
Post by Polymath101 on Apr 20th, 2009, 7:20pm

on 04/16/09 at 06:24:55, rmsgrey wrote:
It's just a matter of methodically listing all the possibilities.

For example, with the triangle, the obvious distinction is between inner and outer rods.

There's only one pattern with two white inner rods.

If the first white rod is outer, then all 6 possible locations are equivalent. If the other rod is inner, that gives three possibilities (forming a 60 degree angle, a 120 degree angle, or parallel and not touching).

If the other rod is outer, then they can both be at the same end of their sides of the triangle (clockwise or counter-clockwise) which only offers one pattern, or at opposite ends, in which case they can be sharing a corner, sharing an edge, or not touching, for three more patterns.

So, putting it all together, that's eight patterns.


For the cube, with three white edges, it's a little trickier because it's in three dimensions rather than two, but a little simpler because of the increased symmetry. A good place to start is by looking at three connected, two connected and an odd one, and all three disconnected.


So...know any other answers?


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