A good friend of mine send me this quiz which was found in compendium at her university. The course was about Mathematical Programming and from what I understood no one could solve this. 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

Done.