# Math Problem

**URL:** <https://boards.straightdope.com/t/math-problem/145835>\
**Category:** Factual Questions\
**Created:** [December 31, 2002, 6:40am UTC](https://boards.straightdope.com/t/math-problem/145835 "2002-12-31T06:40:42Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![sleeping](https://avatars.discourse-cdn.com/v4/letter/s/839c29/32.png) [@sleeping](https://boards.straightdope.com/u/sleeping)\
**Post date:** [December 31, 2002, 6:40am UTC](https://boards.straightdope.com/t/math-problem/145835/1 "2002-12-31T06:40:42Z")

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There is a seven-section bridge across a river. On one side of it, sitting on the first 3 sections, are Alfred, Bert and Carl, and they want to get to the other side. The middle section is empty. On the other side are Eileen, Gertrude and Helen waiting to cross to the other side. Only one person moves at a time. Any person can jump to the next stone if it is empty, or can jump over a person of the opposite sex on to an empty stone. How can all the people cross the river in 15 moves?

X  
X  
X  
STONE  
O  
O  
O

where X is male and O is female.

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**Author:** ![sir\_viks](https://avatars.discourse-cdn.com/v4/letter/s/4af34b/32.png) [@sir\_viks](https://boards.straightdope.com/u/sir_viks)\
**Post date:** [December 31, 2002, 7:10am UTC](https://boards.straightdope.com/t/math-problem/145835/2 "2002-12-31T07:10:35Z")

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Maybe I’m misunderstanding the rules of your puzzle, but I was able to exchange the position of the X’s and O’s in exactly 15 moves. Do they also have to be completely off the bridge as well, or is this arrangement the solution you are looking for?

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**Author:** ![sleeping](https://avatars.discourse-cdn.com/v4/letter/s/839c29/32.png) [@sleeping](https://boards.straightdope.com/u/sleeping)\
**Post date:** [December 31, 2002, 7:30am UTC](https://boards.straightdope.com/t/math-problem/145835/3 "2002-12-31T07:30:05Z")

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No, they just have to be rearranged to be on opposite sides from where they were before. If anyone has found a solution please tell me.

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**Author:** ![sir\_viks](https://avatars.discourse-cdn.com/v4/letter/s/4af34b/32.png) [@sir\_viks](https://boards.straightdope.com/u/sir_viks)\
**Post date:** [December 31, 2002, 7:51am UTC](https://boards.straightdope.com/t/math-problem/145835/4 "2002-12-31T07:51:55Z")

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OK, it’s 3AM, and I apologize for any mistakes in my logic.

In your puzzle, the X’s are in positions 1, 2, and 3, the space is position 4, and the O’s are in positions 5, 6, and 7. Here’s my (sleepy) solution:

X: 3 to 4  
O: 5 to 3  
O: 6 to 5  
X: 4 to 6  
X: 2 to 4  
X: 1 to 2  
O: 3 to 1  
O: 5 to 3  
O: 7 to 5  
X: 6 to 7  
X: 4 to 6  
X: 2 to 4  
O: 3 to 2  
O: 5 to 3  
X: 4 to 5

There. Fifteen moves, positions reversed, and I’m going to bed. Goodnight.

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**Author:** ![sleeping](https://avatars.discourse-cdn.com/v4/letter/s/839c29/32.png) [@sleeping](https://boards.straightdope.com/u/sleeping)\
**Post date:** [December 31, 2002, 8:12am UTC](https://boards.straightdope.com/t/math-problem/145835/5 "2002-12-31T08:12:31Z")

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Thanks, **sir viks**.