The Slothouber-Graatsma puzzle consists of nine pieces that must fit into an open-ended 3 x 3 x 3 box. Three of the pieces are 1 x 1 x 1 cubes and six are 1 x 2 x 2 rectangular solids.
Although you may be tempted to view the solution out of frustration, really challenge yourself to solve it on your own!
The three 1 × 1 × 1 blocks need to be placed along a body diagonal of the box, as each of the 3 x 3 layers in the various directions needs to contain the 1 x 1 x 1 block.
The puzzle is essentially the same if the three 1 × 1 × 1 blocks are left out, so that the task is to pack six 1 × 2 × 2 blocks into a cubic box with volume 27.
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The Step-dissection Puzzle consists of six pieces that can be put together as a rectangular solid arrangement in six different ways. Once you have found one of these arrangements, pull it apart into two congruent halves and see what happens!
Can you make all six arrangements?
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Aims Center for Math and Science Education
