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franz

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There are 6 frogs, and 7 pillars. 3 frogs on the left, and 3 on the right with one empty pillar in the middle. The left ones can only move one pillar right, and the right ones can only move one pillar left. The frogs can jump over each other, effectively moving two pillars. They cannot land on the same pillar which a frog is already on. My question is: how many possible positions are there, and whats the formula to calculate them?

visualized movement of frogs:
 
franz said:
There are 6 frogs, and 7 pillars. 3 frogs on the left, and 3 on the right with one empty pillar in the middle. The left ones can only move one pillar right, and the right ones can only move one pillar left. The frogs can jump over each other, effectively moving two pillars. They cannot land on the same pillar which a frog is already on. My question is: how many possible positions are there, and whats the formula to calculate them?

visualized movement of frogs:
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