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IMSO 2008 Mathematics Contest in Taiwan – Short Answer Question 10

IMSO Maths · IMSO 2008 Mathematics Contest in Taiwan – Short Answer

Question 10

Six of seven positions are occupied by frogs numbered 1, 2, 3, 4, 5, 6 as shown. A frog may move to an adjacent vacant position, or leap over another frog into the vacant position two places away; it may move backward or forward. What is the least number of moves needed so that the frogs occupy the same six positions as initially, but in the order 6, 5, 4, 3, 2, 1 from left to right?

Question illustration