Slothouber–Graatsma puzzle facts for kids
The Slothouber–Graatsma puzzle is a fun challenge where you try to fit special blocks into a box. Imagine you have a small box that is 3 units long, 3 units wide, and 3 units high. Your goal is to pack six blocks that are 1 unit by 2 units by 2 units, and three tiny blocks that are 1 unit by 1 unit by 1 unit, perfectly into this box.
This puzzle was created by Jan Slothouber and William Graatsma, which is where its name comes from. What's cool about it is that there's only one way to solve it, even if you can flip the box around or look at it in a mirror! You can also think of the puzzle as just packing the six 1x2x2 blocks into the 3x3x3 box, leaving three 1x1x1 empty spaces.
How to Solve the Puzzle
Solving the Slothouber–Graatsma puzzle becomes much easier when you know a special trick. The three small 1x1x1 blocks (or the three empty spaces if you're thinking of it that way) must be placed along a diagonal line inside the box.
Think of the box as having three layers in any direction (top to bottom, front to back, or side to side). Each of these 3x3 layers needs to have one of the small 1x1x1 blocks. This is because the larger 1x2x2 blocks always take up an even number of small spaces in any layer. Since each layer has 9 spaces (an odd number), there must be one space left over that a 1x2x2 block can't fill. That's where the 1x1x1 blocks fit!
Other Packing Puzzles
The Slothouber–Graatsma puzzle is a type of "cube-packing puzzle." These puzzles involve fitting different shaped blocks, called polycubes, into a larger box.
There are many other puzzles like this! For example, the Conway puzzle asks you to pack eighteen rectangular blocks into a 5x5x5 box. Another tricky one involves packing forty-one 1x2x4 blocks into a 7x7x7 box. This leaves 15 empty spaces. Just like the Slothouber–Graatsma puzzle, the solution to the 7x7x7 puzzle often involves leaving three long, thin empty spaces (1x1x5) that cross through the box in different directions.
See also
In Spanish: Rompecabezas de Slothouber-Graatsma para niños
