Gallery Problems Exercise

Frog Jump

Work Time

Frog Jump

These two frogs can change places in three moves. The yellow frog starts in the leftmost box.

Rules:

  • A frog can either hop onto an adjacent square, or jump over one other frog to the vacant square immediately beyond it.
  • The yellow frogs can only move from left to right.
  • The green frogs can only move from right to left.
  1. The frogs shown can be interchanged in 15 moves. Explain how.
  2. Now suppose that there are an unequal number of green and yellow frogs. These frogs can be interchanged in 11 moves. Explain how.