# The riddle of pulling the rope

As a puzzle maker, I sometimes receive emails asking me why this or that solution is given a prize when, in his opinion, his solution was as good as the one he took. I may speak of a mathematical problem in which the one who took the prize followed the custom of taking the result only to the third decimal place, while the one who writes to me complains that he was breaking the horns until he reached the tenth, giving clearly what he considers a better answer.

The phrases that accompany each of the three scenes of the rope pulling game shown above are the following:

• The corpulent boys quartet pulls as hard as the five chubby sisters.
• While two chubby sisters and a big boy could maintain their position in front of the thin twins.
• The thin twins and three chubby sisters against a chubby sister and four big boys.

Assuming that in the first two tests there is a tie of forces,

Which side will win the last test?

#### Solution

The strength of the four corpulent boys equals that of the five chubby sisters as shown in the first scene. As shown in the second scene, the thin twins match a corpulent boy plus two chubby sisters so we can simplify things in the third illustration changing the two thin twins for their equivalent in strength, that is, a strong boy and two chubby sisters.

Thanks to this change we now have in the third box five chubby sisters with a big boy competing against a chubby sister plus four big boys. Now we can remove five chubby sisters on one side and four big boys on the other, since the first picture shows us that the strength of these two groups is the same.

This leaves a chubby sister on the right on one side and a big boy on the other, which shows that the team on the left The third frame should win since it has 1/5 of the strength of a big boy more than the other team.