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A Game of Threes
Back in middle school, I had a peculiar way of dealing with super boring classes. I would take my handy pocket calculator and play a "Game of Threes". Here's how you play it:
First, you mash in a random large number to start with. Then, repeatedly do the following:
- If the number is divisible by 3, divide it by 3.
- If it's not, either add 1 or subtract 1 (to make it divisible by 3), then divide it by 3.
The game stops when you reach "1".
While the game was originally a race against myself in order to hone quick math reflexes, it also poses an opportunity for some interesting programming challenges. Today, the challenge is to create a program that "plays" the Game of Threes.
Challenge Description
The input is a single number: the number at which the game starts. Write a program that plays the Threes game, and outputs a valid sequence of steps you need to take to get to 1. Each step should be output as the number you start at, followed by either -1 or 1 (if you are adding/subtracting 1 before dividing), or 0 (if you are just dividing). The last line should simply be 1.
Input Description
The input is a single number: the number at which the game starts.
100
Output Description
The output is a list of valid steps that must be taken to play the game. Each step is represented by the number you start at, followed by either -1 or 1 (if you are adding/subtracting 1 before dividing), or 0 (if you are just dividing). The last line should simply be 1.
100 -1
33 0
11 1
4 -1
1