A French foreign legion general must make a trip across the deserts of Tunis to a remote outpost. He must travel on foot from the nearest town, and the distance is such that it will take a person six days to cover it.

The problem is that a person on foot can only carry enough water and provisions to last him four days. The general can take with him any number of assistants to help him carry the supplies, but they must be fed as well, and cannot be left stranded in the desert.

How will the general make it across, and how many assistants will he need to help him? (Find the smallest number.)

At the point where the last of the assistants to turn back does so, Everyone must have enough supllies to make it (or make it back. Also, the average amount of supplies per person must be no more than three days worth.

This means it occurs at the beginning of the fourth day. The general has three days to continue his journey, annd his aide has three days to return to town.

The third morning the general and that last aide both set out with four days supply. So the aide does nothing to extend the general's survival and is unnecessary.

So the real last aide turned back at the beginning of the third day. He had two days' supply, and two days to get back to town. The general had four days' supply, and four days to get to the outpost.

At the beginning of the second day, they would have needed four day's supply each, which means there must have been a second aide, who turned back here. He would need one day's supplies to return to town, which means he could carry three extra days' supplies, just what the three of them would have needed to get this far.

So the general and two aides start out fully loaded. The first aide turns back the second morning, and the second aide turns back the third morning.

Posted by TomM on 2002-05-30 11:49:47