# DIVISIBILITY GAME

*By toni On 18 August, 2023 · Leave a Comment*

**Resources neeed: **2 dice and pencil and paper for scoring.

**THREES AND FIVES **In turn, players throw 2 dice to determine 2 digits and make a choice between two 2-digit numbers (unless they throw a double). For example, if they get a 4 and a 6, they can make the number 46 or the number 64. They claim their points and explain how they got them by counting the number of divisors but, if they make a false claim, they score zero for that turn. The first player to score 12 points is the winner. The scoring involves exponents: in every game you score two points if the number on the dice is divisible by the square of one of the numbers used in that game, 3 points if divisible by the cube of one of the numbers etc. Players score:

- 1 point if the number is divisible by 3; 1 point if it is divisible by 5;
- 2 points if it is divisible by 9; 2 points if it is divisible by 25;
- 3 points if it is divisible by 27.

For example :

- 64 and 46 are not divisible by 3 or by 5, so this throw scores no points.
- 12 and 21 are both divisible by 3 but not by 5, so whichever the player chooses, the score is 1.
- 15 is divisible by 3 and 5 so it scores 2 points.
- 51 is divisible by 3, but not by 5 or 9 so it scores 1 point.
- 36 and 63 are both divisible by 9 so they both score 2 points.

**TWOS AND THREES or TWOS AND FIVES or ** **TWOS, THREES AND FIVES** **or SEVENS AND ELEVENS** are variants of the game that can be played using the same rules. You will find that, when 2 is included, you quickly score more points, so you could play that you need 24 points to win, or even 36 points. Other variants include divisibility by 13 using any two or three, four, five or six of the prime numbers from 2 to 13.

**THREE DICE VARIANTS:** Playing any of these games with 3 dice, and 3-digit numbers, will be even more challenging. The same rules are used and you score according to the power of the number used in the game that divides the number thrown on the dice.

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