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## Thursday, February 7, 2008

### Crossing the Bridge

Four men must cross an old bridge that spans a raging river. I'm not sure, but it might be the same river that the Victorian couples and the man with the tiger and goat needed to cross as well. The bridge is old and rickety and can only support two men crossing at once. To make matters even worse, it is pitch black and they have only one flashlight to share between them, which means that after two men have crossed one must return with the flashlight. Each of the men has differing abilities and some take more time to cross than the others. The times it takes for each man to cross are: 1 minute, 2 minutes, 5 minutes, and 10 minutes. When crossing in pairs, they can only cross as fast as the slowest man can go.

Can you find a way for all four men to cross in 17 minutes or less?

Anonymous said...

(name each man after the amount of time it takes to cross the bridge)

Step 1) 1 and 2 cross the bride (2 minutes)

Step 2) 1 returns to the beginning side ( 1 minute)

Step 3) 5 and 10 cross the bridge (10 minutes)

Step 4) 2 returns to beginning side (2 minutes)

Step 5) 1 and 2 cross the bridge (2 minutes)

Total time = 2 + 1 + 10 + 2 + 2 = 17 total minutes <>

Anonymous said...

1 and 2 cross - 2 mins
1 goes back - 3 mins
5 and 10 cross - 13 mins
2 goes back - 15 mins
1 and 2 cross again - 17 mins

Easy.

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Anonymous said...

There are exactly two solutions to this problem. One has already been noted above.

Initial State:
[1, 2, 5, 10, 'F'] [] (0)

Solution 1:
[5, 10] [1, 2, 'F'] (2)
[1, 5, 10, 'F'] [2] (3)
[1] [2, 5, 10, 'F'] (13)
[1, 2, 'F'] [5, 10] (15)

Solution 2:
[5, 10] [1, 2, 'F'] (2)
[2, 5, 10, 'F'] [1] (4)
[2] [1, 5, 10, 'F'] (14)
[1, 2, 'F'] [5, 10] (15)

Final State:
[] [1, 2, 5, 10, 'F'] (17)