Problem of the Week 988

A Graph That Will Make You Smile

Alice: I have just come across a graph that is the funniest thing I have ever seen. Just graph the set of points (x,y) such that

1/2 < floor[ mod(floor[y/17] 2^(-17 floor[x] - mod(floor[y],17)), 2) ]

Bob: Let me be sure I understand: the thing inside the outermost "mod" is not an integer. What does "mod" mean here?

Alice: It means the remainder when multiples of 2 are subtracted. So mod(15/4, 2) would be 7/4. The mod function in most computer programs works this way, so don't worry about it.

Bob (some minutes later). You're right. It is not hard to graph. The function on the right is either 0 or 1 so it is just a matter of computing where it is 1. I did it and didn't see any points at all for small values, so I went up a bit and found the following. I fail to get the joke.

Alice: Oh, I forgot to say: You have to graph this for x between 0 and 110 and y between k and k+17, where k is the following 543-digit integer.


Bob (after a break for some more computation): Oh, now I get it! Very funny indeed.

What was the joke?

© Copyright 2003 Stan Wagon. Reproduced with permission.

2 September 2003