Alice thinks of two different numbers, between 1 and 100 (not including), x and y. She then secretly tells Bob their sum (x+y) and Chris their product (x*y). Bob and Chris are astute logicians, and they have the following conversation:
| Chris: | I cannot determine x,y. |
| Bob: | I knew you couldn't. |
| Chris: | In that case, I can determine them. |
| Bob: | Oh, then so can I. |
Provided that Chris and Bob are incredibly intelligent and honest, and every one of their statements is true, what were the numbers? Hint: it helps to use a pen and a piece of paper.