BS2012 wrote:

Mathandski wrote:

In case anyone was curious, here's the joke: according to the rules, everybody missed MOP by 1 point!

We claim that $r = 1$ if and only if your age cannot be written as $3^a 239^b$ . In other words, unless if you are $1, 3, 9, 27, 81, 239, 243, 717, 729, \dots$ years old, $r = 1$ .

The proof comes down to proving two these parts:
Period of F_n modulo 69 is 48

m is a multiple of 48

Unless if you are $1, 3, 9, 27, 81, 239, 243, \dots$ years old, $48 \mid m$ meaning $F_m \equiv F_0 \equiv 1 \pmod{69}$ . With $r = 1$ proved, we plug it in to see the cutoff is $x + 1$ , which is exactly one more than your USA(J)MO score!

what if you are 9 years old, or predict way low

I'm nine so I made MOP