I made a game while at home, and I couldn't solve it for 3 months. The question is below, and the proof is below it. Please let me know if you see any problems!
You start with the equation shown to the above, with a=0 and ± being in the plus state and n being -1. You would then solve the equation. The numbers would vary depending on n, but it would be 1, 5, 21, 85, and so on. You would then make that number be equal to a3±1. So for 5, a would be 2, and the ± would be in the minus state. We can say that for any odd number (z) (This doesn’t work with even numbers.) that a=z∓1/3. You would play starting at n=-1 for each number, and end at n=∞ so the numbers the game “effects” infinite numbers for every number you play with. You would then plug in the answer for each time you change n as “z”. The question is, starting with a=0 and ± being in the plus state and n being -1, can you eventually get every odd number?
