Reversing White and Black

Strategies and Hints

  1. No, a marker on an even number will never land on an odd number. The "even" markers move only on the even squares; the "odd" markers move only on the odd squares. Thus, the puzzle can be solved in two parts.

  2. The diagram shows that the markers on odd-numbered squares can exchange places in 8 moves. The gray arrows show the moves for the white markers on squares 1 and 11. The black arrows show the moves for the black markers on squares 5 and 15.
Solution

The puzzle can be solved in 16 moves, 8 for the "odd" markers and 8 for the "even" markers. Encourage students to invent various ways of recording the moves.