Maths Puzzle

 by Tom Fairman

1. With a two week period to work on the last Maths Puzzle, I hope we all found the answer.

The secretary was stuffing letters into envelopes at random and the questions was what was the probability of him getting 3 letters in the right envelope? The temptation here is to use combinations and binomial probabilities. With a 0.25 chance of getting it right, you can be inclined to use 4C3 x (0.25)^3 x 0.75. However, taking a step back, if three letters are in the right envelopes, then this is sufficient to say that the last letter must also be in the correct envelope, meaning the probability of only getting three right is 0.

2. This week we have a counting puzzle and a story:

On last New Year’s day a mathematician was puzzled by the strange way in which his small daughter began to count on the fingers of her left hand. She started by calling the thumb 1, the first finger 2, middle finger 3, ring finger 4, little finger 5, then she reversed direction, calling the ring finger 6, middle finger 7, first finger 8, thumb 9, then back to the first finger for 10, middle finger for 11, and so on. She continued to count back and forth in this peculiar manner until she reached a count of 20 on her ring finger.

“What in the world are you doing?” her father asked.

The girl stamped her foot. “ Now you’ve made me forget where I was. I’ll have to start all over again. I’m counting up to 1962 to see what finger I’ll end on.”

The mathematician closed his eyes while he made a simple mental calculation. “You’ll end on your ___________,” he said.

When the girl finished her count, she found her father was right.

How did the father arrive at his prediction and what finger did he predict?

Happy Puzzling