3. MATH CLASSAdmitting that I've probably reached my limit, I posted it on XKCD forum (which I don't really frequent) to get input from others. This reply sums up my frustration exactly:

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.

1:20 - Teacher asks if anyone had found the answers. No one had.

1:30 - Teacher asks if anyone had found the answers. No one had.

1:31 - Teacher asks if it would help if he told them if N was odd or even. All 3 say no.

1:40 - Teacher asks if anyone had found the answers. No one had.

1:41 - Teacher asks if it would help if he told them if V was odd or even. All 3 say no.

1:50 - Teacher asks if anyone had found the answers. No one had.

1:51 - Teacher asks if it would help if he told them the sum of N and V. All 3 say no.

2:00 - Teacher asks if anyone had found the answers. All three of them had!

The fact that no reader of Mathpuzzles.com solved the final puzzle makes me reluctant to put the time into it. In theory it's the same process, but I'm not completely confident of how to parse "if it would help".

ETA: And now that I've put some time into it, it looks even more poorly defined than I had originally suspected. I'm really pretty surprised, coming from Robert Kraus and Ed Pegg, Jr.

A possible breakthrough: the envelopes may be unlabeled. A person that sees a number may not know if that's N or V. Along that line, F may also be written as a number 1..5.

Discussion on GreyLabyrinth forum | For what it's worth, the answer is supposed to be SSQ(336)=54.

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