CiSRA Puzzle Competition 2010 - Solutions

3A. Simple Instructions

This puzzle is not about figuring out what to do, since it's all laid out in detail. The difficult part of the puzzle is actually following the instructions!

Firstly, there are some errors in the instructions which are corrected later. So rather than just begin and start assembling cubes, it pays to read through the instructions and use the later information to correct the earlier errors. If you do this, you can simplify the instructions to something resembling this:

• Take two cubes and put the first on top of the second.
• Take another two cubes and put them side by side.
• Take another two cubes and put one on top of the other.
• Take a new cube and put it on the right side of the first cube.
• Take two more cubes and put them next to each other.
• Put another cube on the left side of the third cube.
• Get a new cube and put it behind the seventh cube.
• Take two more cubes, put one in front of the other, and put the back one on top of the fifth cube.
• Sandwich another cube between the eighth and tenth cubes, with the tenth one on top.
• Make a new pile of two more cubes.
• Put another cube on top of the thirteenth cube.
• Take a new cube and put it in front of the twelfth cube and next to the seventh cube.
• Put a new cube behind the eleventh cube.
• Stick a cube underneath the eighteenth cube.
• Put another cube next to the eleventh cube.
• Put a cube on top of the seventeenth cube and next to the ninth cube.
• Add a cube underneath the second cube, another underneath the eighth cube, and another underneath the twentieth cube.
• Put a cube next to the nineteenth cube and on the sixteenth cube.
• Sandwich a cube between the fourth cube and the twenty-second cube.

Now it's a matter of assembling some cubes. This is most easily done by using a real set of small cubes and some method of holding them together - tape is a good idea. Building block toys might also do the trick. Alternatively, you could do it by sketching on paper, or using a computer program to keep track of things, or even by modelling cubes in 3-D software.

In some cases, there are ambiguities. For example, at first you are only told to place cubes three and four "side by side", and not which cube goes on the left or the right. This is resolved later on by the step, "Put another cube on the left side of the third cube," which implies that cube three must be on the left of cube four. All other ambiguities that arise are similarly resolved later.

When you're done, you should have a shape resembling this:

The model is shown in two views so you can see all the cubes labelled with their numbers. The orientation relative to the original instructions is such that cube 1 is on top of cube 2, in front of cube 21, and to the left of cube 7.

It is a simple model of a CHAIR, which is the solution.