### Project 13.1

Devise a fair scheme for eliminating coins in this country.

Here is an alternative question:

Michael Rossides has come up with a scheme for eliminating coins. This scheme involves probability and the fact that most cash registers today are computers. Suppose that every cash register could be programmed with a random number generator; that is, suppose that it were possible to pick a random number from 1 to 99. Rossides’ system works as follows. Suppose you purchase items totaling $15.89. The computer would choose a number from 1 to 99 and then compare it with the cents portion of the purchase. In this case, if the random number is between 1 and 89 the price would be rounded up to $16; if it is between 90 and 99 the price would be rounded down to $15. For example, if you purchase a cup of coffee for $1.20, and the random number generator produces a random number from 1 to 20, the price is $2, but if it produces a number from 21 to 99 the price is $1. Write a paper commenting on this scheme.

### Project 13.2

Find the probability that the 13th day of a randomly chosen month will be a Friday. (Hint: It is not correct to say that the probability is 1/7 because there are seven possible days in the week. In fact, it turns out that the 13th day of a month is more likely a Friday than any other day of the week.) Write a paper discussing this problem.

**References:**

**William Bailey**, “Friday-the-Thirteenth,”* The Mathematics Teacher*, Vol. LXII, No. 5 (1969), pp. 363-364.

**C. V. Heuer**, Solution to Problem E1541 in* American Mathematical Monthly*, Vol. 70, No. 7 (1963), p. 759.

**G. L. Ritter**, et al, “An Aid to the Superstitious,”* The Mathematics Teacher*, Vol. 70, No. 5 (1977), pp. 456-457.