## Sample Problems from Chapter 2

### This starts with such a simple idea, gets into important mathematics (division, sharing, fractions, infinite series), and most young people can and should do it!

1). Share 2 cookies between 3 people. How many does each person get? Each person must get the same amount, and you can't give any to the dog (you must use all the cookies). Use blank 3"x5" cards for the cookies (not circles!) and scissors to cut them.

2). Same problem: share 2 cookies between 3 people, but this time use Brad's method. Brad had finished 2nd grade. He shared the pieces when he could, then cut each leftover piece into 2 equal pieces! Like your scissors are special, they can only cut into 2 equal pieces. Share the pieces when you can, then cut. Keep track of how much each person gets, even when they get zero of a certain size piece!

3). Try other problems like share 1 cookie with 5 people, 2 cookies with 5 people and so forth, use Brad's method and look for patterns!

4). Write a computer program for Brad's method that will give the bimal, that is, get the numerators only (the denominators will be powers of 2) of the resultant infinite series for sharing T cookies with B people.

Send your way of solving the problem and a problem you make up, to
Don Cohen-The Mathman
Ways young people have solved these kinds of problems