Fultiples
Fultiples is a two player Tic-Tac-Toe-like game with a numeric twist. It is played on 10 x 10 grids and each cell of these grids contains a positive integer (these are the numbers you count with).
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As in Tic-Tac-Toe, a player selects cells during their turn and the goal is to connect cells horizontally, vertically, or diagonally. Unlike Tic-Tac-Toe, to win, a player must connect five cells instead of only three (after all, the grids are larger). More importantly, the selection of a cell during a player’s turn depends on the numbers in the number grid: to legally select a cell, its number must be a factor or multiple of the number of the cell chosen by the other player on the immediately prior turn.
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I’ve had fun playing Fultiples with several of my students and they enjoy it too.
Getting Started
You need three things to play:
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A 10 x 10 number grid. If you choose to download a grid (see left), there are beginning, intermediate, and advanced grids to choose from. Beginning grids contain only numbers less than or equal to 50, intermediate, less than or equal to 100, and advanced, less than or equal to 200. Or you can generate one online here: generate grid online.
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One six-sided die to determine who goes first.
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Something to mark selected cells with so that the numbers are still visible. I have a collection of translucent, glass markers so that the same grid can be used over and over, but you can also mark on the grids directly using colored pencils or pens or just graphite pencils with different kinds of marks for the two players.
If necessary, please see the formal instructions for further details on the flow of play.
The above is all you need to begin playing but here is some additional information about where the grids come from to help you select one.
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Each grid is based on some set of prime numbers. Recall that a prime number is one that is evenly divisible only by one and itself. So two, seven, and eleven are prime numbers, but six and eight are not since eight, for example, is evenly divisible by two and four as well as by one and itself.
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To say each grid is based on a set of prime numbers is to say every number in a grid is a multiple only of members of this set and no other prime numbers. Thus if a grid is based on the prime numbers two and three, every number in the grid is a multiple of either two or three or both. So this grid can contain the numbers six ( = 2 x 3) and twelve ( = 2 x 2 x 3) but not fifteen, since fifteen is also a multiple of five (a prime number). But note that fifteen would be allowed on a grid that was based on the set of prime numbers two, three, and five.
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The set of prime numbers for a grid is written at the top of each one.
Here are the formal instructions:
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Rules:
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1. Players agree on a grid to use. Grids can be generated online here: generate grid online; or downloaded above.
2. After a grid is chosen, each player rolls a six-sided die and the one with the higher roll is the first player. In case of a tie, roll again.
3. Each player picks a different color or shape for marking or shading their cells.
4. The first player marks or shades the cell of any number on the grid to start the game.
5. The players take turns marking or shading cells. Each marked or shaded cell must contain a number that is a factor or multiple of the number in the immediately previously marked or shaded cell.
6. Continue in this manner, taking turns, until one player gets 5 in a row. You can get 5 in a row horizontally, vertically, or diagonally.
7. Once a player gets 5 in a row, that player is the winner!
Additional Options:
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Time Limit: A time limit can be chosen to:
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- Make the game more difficult.
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- Take the advantage away from people using calculators.
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Do keep in mind that grids based on larger prime numbers or containing larger numbers might need a longer time limit since calculations will be harder.
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If a time limit is chosen, each player (including the first player who starts the game) has to complete their turn within the time limit. If they fail to do so, they lose their turn and the other player gets to go.
Clarifications
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- When starting a new game, another dice roll determines who starts.
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- After a player takes their turn, you don't have to wait for the time limit to finish. Instead, the timer restarts and it is the next player's turn.
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- A prime number is a number that can be divided without a remainder only by one or itself. For example, three and seven are prime numbers but eight, since it can be divided without remainder by two and four as well as one and itself, is not.
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- When a player chooses a cell, the number in the chosen cell must always be a factor or multiple of the number in the previously chosen cell. It doesn't matter which player selected the immediately previously chosen cell.
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- A factor of a number divides into that number without remainder.
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- A multiple of a number is that number times any positive integer including one.
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- Positive integers are the numbers you count with.
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Personal Links
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| Name | Links |
|---------------|---------------------------------------|
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| Jackson Novak | https://www.oglo.dev |
| Glen Meyer | http://www.themathematicalcopilot.com |
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The source code for the online grid generator: https://codeberg.org/Oglo12/fultiples-docs
Credits
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Initial Inspiration For Fultiples:
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University of Cambridge Nrich Team's [Factors and Multiples Game] (https://nrich.maths.org/games/factors-and-multiples-game)
Original Game Idea And Boards Created By:
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Glen Meyer
Game Extended And Worked On By:
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Glen Meyer
Jackson Novak
Ezra Novak
Algorithms Developed By:
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Jackson Novak
Glen Meyer
Software Written By:
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Jackson Novak
Play tested By:
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Glen Meyer
Jackson Novak
Ezra Novak
Jet Bostad