The puzzle is as follows:
The figure from below belongs to a didactical toy which is comprised of 32 congruent wood pieces as indicated in the figure. Each piece is made up by three cubes whose edges measure 3 centimeters. If by using only these you want to make the maximum amount of compact cubes as possible. How many of these pieces you will not use?
The choices given are as follows:
- 5 pieces
- 3 pieces
- 4 pieces
- 9 pieces
This puzzle it seems to stem from an old APA IQ exam from mid 1990s on psychometry for intelligence which is based on Leon Thurstone's and Raymond Catell IQ test timed cards.
I'm not sure how to solve it.
The question does not ask directly for the number of pieces, but instead in reverse for the number of pieces which will be unused or discarded to make cubes with only the pieces shown.
This part requires spatial visualization, which I lack, so an auxiliary drawing or figure would be helpful for any solutions.
In other words how to make a cube by using only the piece shown? The source doesn't indicate that the cubes can be split and rearranged in a line or any other shape. So I'm assuming that the intended solution does not modify the shape given.
Moving just this piece around I made a 3×3 cube. That is using six of these pieces.
In total it would be 27 cubes.
There would be 32-27=5 unused cubes. But this begs a question. Can these cubes be split or not?
Had this toy be composed of single cubes, I wouldn't bothered to assemble them in any way. I don't know how to correctly interpret the problem
Since 5 is one of the choices (#1) given, it might be the answer. But I can't say for sure. Perhaps another way to see this problem exists.
Therefore I'm requesting help. Please include drawings in answers so I can better visualize the solution to this puzzle.