# Math Club Riddle

## Mathematics and Computer Science

Taylor Hall

308 E. University Street

Wooster, OH 44691

Phone: 330-263-2478

jmiddleton@wooster.edu

## 2017-2018

Every correct solution earns one entry in the end-of-year drawing for Math goodies!

Email Solutions to cowmathclub@gmail.com by 8:00 pm Friday November 17.

## Riddle #3 - Table Dimensions

A round table is pushed into a corner of a rectangular room so that the table touches both walls and its feet are firmly on the ground. Suppose that there is a point on the perimeter of the table which is 10 inches from one wall and 5 inches from the other. What is the diameter of the table?

## Riddle #2 - Meeting Up

Two friends agree to meet at the library, but each has forgotten the time they were supposed to meet. Each remembers that they were supposed to meet sometime between 1:00pm and 5:00pm, and they each independently decide to go to the library at a random time between 1 and 5, wait for 30 minutes, and leave if the other doesn't show up. What is the probability that they meet during this 4 hours period?

## Riddle #1 - Ten Sentences

Congratulations problem solvers: Colleen O'Sullivan, Carlos Owusu-Ansah, Carson Geissler,Zhirui Zhang, Maya Lapp

Most elegant solution by Colleen O'Sullivan: Statement 9 is true. As each statement gives a different number of true sentences and says exactly (not at least), we know that only one statement can be true. The only statement that says that 9 of the 10 statements are false and only one is therefore true is statement 9.

Which (if any) of the following sentences are true? Explain your reasoning.

1. Exactly one of these ten sentences is false.
2. Exactly two of these ten sentences are false.
3. Exactly three of these ten sentences are false.
4. Exactly four of these ten sentences are false.
5. Exactly five of these ten sentences are false.
6. Exactly six of these ten sentences are false.
7. Exactly seven of these ten sentences are false.
8. Exactly eight of these ten sentences are false.
9. Exactly nine of these ten sentences are false.
10. Exactly ten of these ten sentences are false.