Knight’s Move challenges are quite popular. They can involve one more more knights and varying spaces that the knight has to traverse.
Our challenge is a simple Knight’s tour, where the knight should land on each square exactly one time to complete it. We are adding a way of keeping track that gets us to practise arithmetic.
Each time the knight moves from one number to another, it effectively performs an operation. This is what we call a simple function that turns one number into another number in arithmetic. On our grid, there are only so many operations that a knight’s move can create. These are mostly addition or subtraction operations. See if you can find all the possible addition and subtraction operations that can be made by a knight’s move on our 5 by 5 board.
Are there any knight’s moves that could be multiplication or division? What about raising to the power or squaring, can you find one or prove that it’s not possible?
Download the pdf with more support for trying the challenge. How might this change on a 4 by 4 board or a 6 by 6 board?