# Problem Solving Puzzles

=== by Bob Sutherland ===

## Here are a few simple problems to give your brain some exercise.

### Foremen & Workers

There are three workmen and three foremen working at a job site. After they finish working at the first job site they have to move to a second job site a few kilometers away. They have one utility truck that can hold a maximum of two people. All of the men have valid driver's licenses and know how to drive the utility truck. Plan the trips for the men to move them from the first job site to the second job site using the utility truck. Be aware that it is company policy that every workman must be supervised by at least one foreman at all times. Therefore no workman may be left alone at a job site or driving the utility truck without a foreman being there to supervise him.

Hint: Do not try to solve any of these problems in your head. The trick is trying to figure out how you can use pencils, paper and any other objects you might have nearby to help you solve the problems.

### Jealous Girlfriends

On a hot summer weekend there are three young couples who would like to go to the beach for a picnic. It is quite some distance to the beach and the only vehicle they have available for transportation is a motorcycle. Everyone has a motorcycle driver's license and can drive the motorcycle. The motorcycle can hold a maximum of two people. Plan the trips for the motorcycle to take all of the couples to the beach. There is one special consideration. All of the girls are extremely jealous. They trust the boys to be together. But none of the girls will trust her own boyfriend to be with either of the other two girls unless she is there with him.

Comment: If you have a hangup about the fact that I randomly picked the girls to be the jealous ones then change the gender so that the boys are the jealous ones. I do not care. I just want to know if you can solve the transportation problem.

### How Many Triangles?

How many triangles can you count in the first arrowhead diagram?

Hint: There are triangles of many different sizes in the diagram with small triangles joining together to form larger triangles. Make sure you find and count all of them.

Just in case someone assists you with counting the triangles in the first diagram I have created a new challenge by moving one of the lines. How many triangles including all the different sizes can you find and count in the second arrowhead diagram?