# Varsity Math, Week 122

## ________________

A problem in spatial visualization and another related to tennis have come to the coach’s attention.

## ________________

### Rolling Circles

Two circular disks have radii of 12 and 14. The larger disk is held fixed while the smaller disk is allowed to roll around the outside of the larger disk without slipping. In their starting positions, point P on the smaller disk coincides with point Q on the larger disk.

How many rotations of the smaller disk must occur before points P and Q coincide again?

### Minimum Racket Wear

Having won the first set of a singles match at the Australian Open, Rafael Nadal is just starting the second set.

What is the least number of times his racket could have hit the ball during the first set? You will need to know that if a player, in two attempts to serve on a point, swings and misses both times, that player loses the point. No tricks are involved here.

## Solutions to week 121

In Tennis Exhibition, Rafa and Roger played in set number 13. The answer to Losing Streak is 52 points.

Tennis Exhibition answer explained:
Since two players participate in each set there are 19 sets played in all. The only way for Novak to play just 9 sets is to play in the even numbered sets and lose each time. Thus, Rafa and Roger played in set number 13.

Losing Streak answer explained:
Maria could win the first set and go ahead 5-0, 40-0 in the second set. She could then lose the next 52 points to be down 0-5, 0-40 in the third set. It takes 5 points to lose the game to get to 1-5 and another 24 points to lose the set to get to 5-7. It then takes another 23 points to reach 0-5, 0-40. She could then win the third set and the match from that situation.

## Recent Weeks

Links to all of the puzzles and solutions are on the Complete Varsity Math page.

Come back next week for answers and more puzzles.