# How to cross a river

A detachment of 100 soldiers must pass a very deep river, but the bridge is destroyed. Suddenly the commander sees two children sailing in a small boat near the shore but the boat is so small that it only fits one soldier or two children and no one else.

How many boat trips were necessary so that all the soldiers could cross the river with the boat and how did they do it?

#### Solution

Children cross the river with the boat. One of them stays on the other shore and the other returns with the soldiers and leaves the boat. On the boat sits a soldier who passes to the other shore. The boy on that shore climbs into the boat and returns with the soldiers. The two children then get on the boat and go to the other shore. One of them stays in it and the other one returns with the soldiers and leaves the boat. In the boat sits the second soldier who passes to the other shore.

With this system, after every two boat trips across the river a soldier passes to the other shore so in total they will need 200 trips.