jrice15 / gamey_bromey

The strangest, most elusive Open Problem ever to spontaneously arise out of a third-grader

GAMEY BROMEY

The strangest, most elusive Open Problem ever to spontaneously arise out of a third-grader

What is it?

John Brode somehow made up a formula for computing numbers from any combination of alphanumeric or puntuation characters, in the third grade. It is perfectly internally consistent (ie, he's not just making it up). He can calculate them extremely quickly, but the answers do not follow an easily discernable pattern.

How does it work?

We know that the characters G, A, M, E, and Y are worth points, while the rest are not. Other than Y, which is worth -1, they are all worth 1. However, when they are grouped, strange patterns appear. To simplify things, all characters GAME are denoted by an A, while the rest are denoted by a T (and Y by Y, of course).

What do we know?

We know leading T's are irrelevant. Thus the score can always be computed by starting from the first group of A's. This means that we can unambigously denote the word "Tallahassee" (TATTATATTAA) by counting the A's and T's as groups and starting with the first A's, leaving ATTATATTAA. This can be unambigously represented as the list 1_2_1_1_1_2_2 (which becomes especially helpful when dealing with hypothetical words nearing 50 characters in length). In knowns.ts you will see over 10,000 of such combinations, all with their verified answer. One would think that it would be trivial to solve the problem if that much data had been collected. One would be wrong.

We know there is something to do with alternation. Patterns that arrise when changing one letter group at a time consistently appear as 010101 or 0,2,1,2, etc. Even-odd-ness is important, we think.

Why the name?

GAMEY as the point-value letters. BROMEY is just mashing GAMEY with the originators last name, Brode

gamey_bromey's Issues

no 'Y' support