# Side by Side

## Instructions

On these pages you will find a series of Math Puzzles called the "Side By Side" puzzles. Each puzzle consists of a series of seven numbers, which may include repeated numbers. The numbers will appear in a grid like the one shown below:

Your job will be to rearrange the numbers in that row so the result conforms to a "rule". Each game has its own rule. Rearrange the numbers by clicking on one number, then clicking the position where you want to move it. The tile you selected will slide to the new location you clicked, and all the tiles between the old and new location will slide one space in the opposite direction to make room for the tile being moved. Each time you move numbers, the game will inform you of your progress by showing you numbers that don't match the rule.

*can*be solved, and most can be solved in more than one way.

### Side By Side Addition Game

In this version of "Side By Side", you must arrange the numbers so that no two numbers which are side by side add to make one of the other numbers in the row.

### Side By Side Factors Game

In this version of "Side By Side", you must arrange the numbers so that every pair of side by side numbers is relatively prime. In other words, any two numbers which are side by side cannot have any common factors besides 1.

### Side By Side Expert Game

This game is very similar to the Addition Game, except that in addition to the rule that no two side by side numbers can add to make another number in the row, there is a *second* rule, that no side by side numbers can *subtract* to make another number in the row.

## How The Puzzles Were Created

The puzzles were created using a random process; a program was written to randomly generate a puzzle, and then try to randomly solve it. The program attempted to solve each puzzle one thousand times, and kept track of how many valid solutions were found. In each case, if there was at least one solution found and no more than ten solutions found, the puzzle was stored in a database.

Each version of the game (Addition, Factors, and Expert) has approximately 400 puzzles.