A good friend of mine send me this quiz which was found in compendium at her university. The course was about Mathematical Programming. I have copied the quiz directly.

**The assignments:**

Warning, this assignment is rather hard. It should have been used in a Microsoft during hiring interviews.

Four persons have to cross a bridge. The times each needs to cross it are:

- 5 min
- 10 min
- 20 min
- 25 min.

It is dark and they only have one lamp, we have the following constraints:

- the bridge can only be crossed if one has a lamp, while it is too dark.
- 2 persons at most are allowed to be on the bridge at the same time.
- the speed of a pair is determined by the speed of the slower person.
- the lamp can last only an hour.
- the lamp cannot be thrown.

Can you figure out a way so that the four men can cross the bridge in 60 minutes.

**Solution**

Here is how I solved it. It is a classical problem where you need to move back and forth a couple of times.

Crossing time for each person

A – 5 minutes.

B – 10 minutes.

C – 20 minutes.

D – 25 minutes.

The plan is as the following

Time | Start | Movement | End |
---|---|---|---|

0 minutes | A B C D | ||

10 minutes | C D | A & B walks over | A B |

15 minutes | A C D | A walks back | B |

40 minutes | A | C & D walks over | B C D |

50 minutes | A B | B walks back | C D |

60 minutes | A & B walks over | A B C D |

Done.