Make Numbers. Win Prizes. Get Famous.

Welcome to TriX Game! The object of the game is to produce a single number. You always start with the number 1. On each of your turns you can apply one of two rules to your current number to construct another number, which becomes your new current number. The rules are called Inflate and Deflate, but we won't ruin your fun by telling you what they do. (You can easily figure that out by experimentation.)

It may require some study and investigation on your part to come up with an efficient strategy for beating this game at the higher levels of difficulty. (The level of difficulty corresponds roughly to the minimum number of turns required to win the game.)

Game Components

As described in the Introduction, this game illustrates the basic features of a formal proof system.

• Toys: The toys in this game consist of a single positive whole number.
• A Goal: The goal is a randomly selected positive number. Your objective is to construct this number.
• The Starting Position: The starting position in this game is the number 1. This is the only toy on your list when you begin the game.
• The Rules: There are two legal moves in this game called Inflate and Deflate. It is up to you to determine what they do. Note that you can always Inflate your current number but you can only Deflate certain numbers.
• Inputs: The input for both Rules consists of the current number. The current number is always the last number listed on the table. You can undo a move and go back to a previously constructed number by pressing U
• Output: The output is the number produced by either Inflating or Deflating the current number. This number is added to the bottom of the list and becomes the current number. If it matches the goal, you win!

The Math Behind the Fun

This game is closely related to a famous unsolved question in mathematics. In particular, it is not known whether this game can be won for EVERY positive whole number goal. It has been demonstrated by computer that this game can be won for all goal numbers less than $10^{17}$. If you can prove that there is a strategy for winning this game there are cash prizes available and you will certainly become famous! Remember that it isn't enough to come up with a strategy that seems to win every time you play the game, you must prove beyond a doubt that your strategy would win the game no matter what positive whole number is selected as the goal (even if the number is too large to actually fit in a computer).