   SEARCH HOME Math Central Quandaries & Queries  Question from Lisa, a parent: Here is the problem of the week my son came home with and we can not figure it out. Billy Club was assigned the task of putting numbers on all the playground balls used during daily recess. Billy will number the balls using the following rules: 1. It will be a 4-digit number. 2. The digit in the thousands place will be a 1 or a 2. 3. The digit in the hundreds place will be a 2, 4, or 6. 4. The digit in the tens place will be an odd number. 5. The digit in the ones place will be greater than six. How many balls can Billy number if he follows these rules? Lisa,

2. The digit in the thousands place will be a 1 or a 2.

How many choices here?

3. The digit in the hundreds place will be a 2, 4, or 6.

How many choices here?

4. The digit in the tens place will be an odd number.

How many choices here?

5. The digit in the ones place will be greater than six.

And how many choices here?

Now, all these choices are independent, so the final answer is obtained by multiplying.

Good Hunting!
RD     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.