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
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.
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.