Example 2

When the net is folded, which cube will be produced? Assume the back side of the net is white.

In this example, it may be easier to determine which cubes will not be produced. Try to determine reasons a cube cannot be made from a net.

  • Two colours on opposite sides of the cube will not touch when the net is folded.
    • In B, red is beside yellow. This is not possible because the net has a light blue between those colours.
    • In D, purple is beside green. This is not possible because the net has a yellow between those colours.

  • The colours need to be ordered correctly.
    • On the net, if you travel from light blue to yellow and then turn left you will be on purple. On cube C, if you travel from light blue to yellow and then turn left, you land on green, so cube C is not possible.

You know it cannot be B, C, or D, so it must be A or E. You are down to two choices from five. Try to determine which of the remaining cubes is correct.

For further examples of using reasoning to solve problems see pp. 45–48 of Principles of Mathematics 11.

Reasoning can be an extremely useful skill when solving problems. Unfortunately, it is easy to make a mistake when reasoning, which can lead to incorrect or unsupported conclusions. Sometimes, even when all of your reasoning is done correctly, you still end up with a paradox. Paradoxes can be fun to play with, but they can also point out flaws in logic. In general, care needs to be taken when reasoning to ensure conclusions are well-founded.