Quite some time ago (9 years!?) I invented a quick little classroom game called Damult Dice. It’s a dice game played with three dice. You roll, choose two to add, and multiply the sum by the third. In general, you’re trying to get as many points as you can per turn, though readers suggested many variations and improvements!

This week I received an email from a teacher named Christine who had spun off a variation she called *Damult Dice Division*. I thought it was a clever version, and wanted to share it here.

#### How to Play (the basic version)

On your turn, roll 3 dice. Choose 2 to make a 2-digit number, and divide that number by the number on the remaining die. Your score is the quotient, rounded down to the nearest whole number. You get a +10 point bonus if the quotient is a whole number (i.e., if there’s no remainder when you perform the division).

Example. You roll 2, 5, 6. You have the following options for moves:

- 25 ÷ 6: 4 points
- 26 ÷ 5: 5 points
- 52 ÷ 6: 8 points
- 56÷2 = 28. Plus the 10 point bonus is 38 points!
- 62÷5: 12 points.
- 65÷2: 32 points.

I like that 10 point bonus, because it prevents an algorithm (take the 2 biggest numbers and divide by the smallest) from determining your choice every turn, which is the weakness of the original Damult Dice for extended play.

Here’s Christine’s writeup and score sheet. She plays to 400 points, but I think playing to 150 or 200 points is probably sufficient.

#### My Variation of Damult Dice Division

In my original writeup of Damult Dice, Jason Buell noted the downside that while one person takes a turn the others in the game have nothing to do. So here’s a competitive variation of Damult Dice Division that gives everyone something to do.

#### How to Play Damult Dice Division All-Play

Take turns as the roller. Roll three dice. Everyone writes down a division problem formed by taking a 2-digit number and dividing by the third, along with the answer (either in decimal, fraction, or remainder form). The roller gets to score their move as per the original game, by taking points given by their answer, rounded down to the nearest whole number, and taking a 10 point bonus if there was no remainder.

After the roller has scored, all other players reveal the equation they wrote down. If a player was the only one to write down a certain equation, they get to score it. If two or more players wrote down the same equation (including the roller), they don’t score any points. The roller’s equation cancels out others as well.

#### Example turn

In a six-player game, it is player 1’s turn to be the roller. Player 1 rolls 2, 5,6. Everyone writes down an equation using those numbers.

The roller reveals their equation: 56 ÷ 2 = 28. This comes out to a whole for a 10 point bonus, so the roller gets 38 points.

Next the other players reveal their equations.

- Player 2: 65 ÷ 2 = 32.5 (0 points)
- Player 3: 65 ÷ 2 = 32.5 (0 points)
- Player 4: 56 ÷ 2 = 28 (0 points)
- Player 5: 26 ÷ 5 = 5.2 (5 points)
- Player 6: 25 ÷ 6 = 4.5 (0 points)

Players 2 and 3 both wrote the same equation, so they don’t score any points. Player 4 wrote the same equation as the roller, so doesn’t score any points. Player 6 wrote an incorrect equation, so doesn’t score any points. But player 5 was the only player to write that equation, and it’s correct. So player 5 scores 5 points.

This version should get every student writing equations, and also gives everyone something to do on every turn. And of course, you can play with 1-sided dice, or with four dice (forming a 3-digit number to divide by a 1-digit number) for a more advanced game.

Does this look like something you would play with your students? Let me know how it goes!