## Wednesday, January 27, 2010

### Unsolvable puzzle?

I will admit that I've tried to solve this puzzle twice now and failed miserably both times.
3. MATH CLASS

A high school math teacher chose three of his best students to conduct a little experiment. He said, "I have chosen a three-digit number, N, with the first digit not more than the second and the second not more than the third. I also have chosen a function, F(N), which is one of these five functions:

(1) SUM(N) = The Sum of the digits of N.
(2) PROD(N) = The Product of the digits of N.
(3) SSQ(N) = The Sum of the Squares of the digits of N.
(4) SSC(N) = The Sum of the Cubes of the digits of N.
(5) LCM(N) = The Least Common Multiple of the digits of N.

"I then calculated the value, V = F(N), and have written the three items, N, F, V, each on a separate piece of paper and will give one to each of you. You must try to determine the other 2 items not on your paper. You may use your computers, but cannot collaborate. Don't turn in your answers until I ask for them. Don't worry about any unfair disadvantage of which item you get, this is not a competition, only an experiment. Just make your lists and we'll see what happens!"

Here is what happened:
1:00 - Students begin working.
1:31 - Teacher asks if it would help if he told them if N was odd or even. All 3 say no.
1:41 - Teacher asks if it would help if he told them if V was odd or even. All 3 say no.
1:51 - Teacher asks if it would help if he told them the sum of N and V. All 3 say no.