I’ll cross that moat

I’ll cross that moat

I need to enter a castle that is surrounded by a five meter wide rectangular moat filled with water. I have an aversion for getting wet and only have two 4.8 meter long planks with no rope, nails, etc. How do I get across?

Communicated by G. Mejia.

This is one of those questions where it may be easier to try to visualize the problem on paper than to try to solve it mentally. We decide to draw a diagram. We make this choice because the information in the problem is geometrical in nature, so a diagram could make the solution easier to see.

 

FIRST THOUGHTS

We decide to draw our moat in a rectangular shape, since we are operating under the assumption that most castles (or at least ones in made-up math riddles) are rectangular. When we reach the first corner, we see a change in behavior. These four points are different than the other points. Perhaps we should focus our attention here….

 

SECOND THOUGHTS

We can put one of the planks lying across the corner. Now what?

 

THIRD THOUGHTS

Now rest the other one on top of the first plank. This way, the 4.8 meters of the second plank will be completely supported by the first plank and the ground. See the attached diagram.

This problem demonstrates the importance of diagrams in solving problems involving physical situations that can occur in the real world. Sometimes it is easiest to draw a diagram, and the solution falls right out without much extra work.