DIVISIBILITY GAME

The only resources needed are 2 dice and pencil and paper for scoring. 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 choose the number 46 or the number 64. Scoring involves exponents. In every game you score 1, 2 or 3 points according to whether the number on the dice is divisible by a number used in that game, or divisible by a square or cube. In the THREES AND FIVES Game players score  1 point if the number is divisible by 3 or 5, 2 points if it is divisible by 9 or 25; and 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.

Other variants of the game that can be played using the same rules include TWOS AND THREES or TWOS AND FIVES or  TWOS, THREES AND FIVES or SEVENS AND ELEVENS . 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.