# Roll3Dice

Roll3Dice is our new initiative aimed at getting parents and children to learn together in a very informal and enjoyable way.

It is vitally important that parents and children can spend time together educationally and this is a simple and fun way of doing this and improving a child’s number skills too.

Introduction

Whereas most parents have read to their young ones at some point, it’s unlikely that they have played a maths game or done a fun arithmetical equivalent.

As the name suggests, the idea simply involves rolling three dice. Roll3Dice then encourages parents and children to work together to try and solve the maths problem in hand using the three numbers and the four arithmetic operations.

How it works

Step 1: Roll three normal dice, each containing the numbers 1-6.

Step 2: Now, work together with pencil & paper to try and find all possible answers that can be made from 1-10 when using these three numbers once each and + – × ÷ available.

Play Roll3Dice a few evenings each week and see your child’s maths confidence, skills and creative thinking dramatically improve.

Roll3Dice ideas

After rolling the dice, the usual activity is for both adult and child to try and figure out the possible answers together as a team, but as the child gets more familiar and experienced the two players could take turns to find one answer each until one of the players stumbles and loses the game.

Alternatively, after rolling a particular combination of numbers, the two players could browse at the possible answers below and challenge each other in a competition format to work out how to arrive at these answers in a specified time, but this period could decrease the more times Roll3Dice is played!

The possibilities are endless; parents, grandparents, carers and teachers will make up their own fun mathematical games involving the three numbers and their solutions.

All 56 combinations when playing Roll3Dice are shown below, together with the number of possible answers from 1 to 10 (in brackets) and the answers themselves.

The 1-2-4 combination shown in bold is the only one where all ten answers are possible:

•  1-1-1      (3)     1, 2, 3
•  1-1-2     (4)     1, 2, 3, 4
•  1-1-3     (6)     1, 2, 3, 4, 5, 6
•  1-1-4     (6)     2, 3, 4, 5, 6, 8
•  1-1-5     (6)     3, 4, 5, 6, 7, 10
•  1-1-6     (6)     3, 4, 5, 6, 7, 8
•  1-2-2     (6)     1, 2, 3, 4, 5, 6
•  1-2-3     (9)     1, 2, 3, 4, 5, 6, 7, 8, 9
•  1-2-4   (10)   1, 2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-5     (9)     2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-6     (9)     2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-3-3     (8)     1, 2, 5, 6, 7, 8, 9, 10
•  1-3-4     (6)     1, 2, 6, 7, 8, 9
•  1-3-5     (7)     1, 2, 3, 7, 8, 9, 10
•  1-3-6     (7)     1, 2, 3, 4, 8, 9, 10
•  1-4-4     (5)     1, 2, 7, 8, 9
•  1-4-5     (5)     1, 2, 8, 9, 10
•  1-4-6     (5)     1, 2, 3, 9, 10
•  1-5-5     (4)     1, 2, 9, 10
•  1-5-6     (3)     1, 2, 10
•  1-6-6     (2)     1, 2
•  2-2-2    (5)      1, 2, 3, 6, 8
•  2-2-3    (7)      1, 2, 3, 4, 7, 8, 10
•  2-2-4    (7)      1, 3, 4, 5, 6, 8, 10
•  2-2-5    (6)      1, 4, 5, 6, 8, 9
•  2-2-6    (8)      1, 2, 4, 5, 6, 7, 8, 10
•  2-3-3    (7)      1, 2, 3, 4, 7, 8, 9
•  2-3-4    (8)      1, 2, 3, 4, 5, 6, 9, 10
•  2-3-5    (7)      1, 4, 5, 6, 7, 9, 10
•  2-3-6    (6)      1, 4, 5, 6, 7, 9
•  2-4-4    (7)      1, 2, 3, 4, 6, 8, 10
•  2-4-5    (6)      1, 2, 3, 6, 7, 10
•  2-4-6    (7)      1, 2, 3, 4, 5, 7, 8
•  2-5-5    (5)      1, 2, 3, 5, 8
•  2-5-6    (7)      1, 2, 3, 4, 7, 8, 9
•  2-6-6    (6)     1, 2, 3, 6, 9, 10
•  3-3-3    (5)     2, 3, 4, 6, 9
•  3-3-4    (6)     2, 3, 4, 5, 9, 10
•  3-3-5    (4)      1, 4, 5, 6
•  3-3-6    (6)      1, 3, 5, 6, 7, 9
•  3-4-4    (5)      2, 3, 4, 5, 8
•  3-4-5    (7)      2, 3, 4, 5, 6, 7, 8
•  3-4-6    (6)      1, 2, 5, 6, 7, 8
•  3-5-5    (5)      2, 3, 4, 7, 10
•  3-5-6    (7)      2, 3, 4, 7, 8, 9, 10
•  3-6-6    (5)      2, 3, 4, 8, 9
•  4-4-4    (4)      2, 3, 4, 5
•  4-4-5    (4)      3, 4, 5, 6
•  4-4-6    (6)      2, 5, 6, 7, 8, 10
•  4-5-5    (4)      3, 4, 5, 6
•  4-5-6    (7)      2, 3, 4, 5, 6, 7, 10
•  4-6-6    (5)      3, 4, 5, 8, 9
•  5-5-5    (4)      2, 4, 5, 6
•  5-5-6    (4)      4, 5, 6, 7
•  5-6-6    (4)      4, 5, 6, 7
•  6-6-6    (4)      2, 5, 6, 7

We’d love to hear from you whether you have any queries or issues regarding the answers or even if you just want to share your own innovative ways of playing Roll3Dice.

Please feel free to email us at paul@7puzzle.com or send a tweet to @7puzzle. Learning together can be very rewarding.

The next step

If, as a parent/carer/teacher, you have seen the benefits of Roll3Dice and want to push on, we fully recommend the following activity. It’s a little more challenging, but very similar in concept.

Mathematically Possible online

To move onto a more advanced number puzzle, click this for details of our Mathematically Possible online programme that offers the same as above, but can randomly generate three numbers from 1-10 instead of just 1-6. The programme can be adjusted so players can choose their own group of three numbers and list all the possible target answers in any range as instructed by the user.

You may still wish to keep things simple and use the three numbers which replicate normal dice (1-6) but want to test your kids on a wider range of answers than above.

For instance, if you choose the increase the target range to 1-30, all the possible combinations are shown here:

•  1-1-1      (3)     1, 2, 3
•  1-1-2     (4)     1, 2, 3, 4
•  1-1-3     (6)     1, 2, 3, 4, 5, 6
•  1-1-4     (6)     2, 3, 4, 5, 6, 8
•  1-1-5     (6)     3, 4, 5, 6, 7, 10
•  1-1-6     (6)     3, 4, 5, 6, 7, 8, 12
•  1-2-2     (6)     1, 2, 3, 4, 5, 6
•  1-2-3     (9)     1, 2, 3, 4, 5, 6, 7, 8, 9
•  1-2-4    (10)    1, 2, 3, 4, 5, 6, 7, 8, 9, 10
•  1-2-5    (12)    2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15
•  1-2-6    (14)    2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 18
•  1-3-3     (9)     1, 2, 5, 6, 7, 8, 9, 10, 12
•  1-3-4    (11)     1, 2, 6, 7, 8, 9, 11, 12, 13, 15, 16
•  1-3-5    (13)     1, 2, 3, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20
•  1-3-6    (14)    1, 2, 3, 4, 8, 9, 10, 12, 15, 17, 18, 19, 21, 24
•  1-4-4    (10)    1, 2, 7, 8, 9, 12, 15, 16, 17, 20
•  1-4-5    (12)    1, 2, 8, 9, 10, 15, 16, 19, 20, 21, 24, 25
•  1-4-6    (13)    1, 2, 3, 9, 10, 11, 18, 20, 23, 24, 25, 28, 30
•  1-5-5    (10)    1, 2, 9, 10, 11, 20, 24, 25, 26, 30
•  1-5-6     (9)     1, 2, 10, 11, 12, 24, 25, 29, 30
•  1-6-6     (6)     1, 2, 11, 12, 13, 30
•  2-2-2    (5)      1, 2, 3, 6, 8
•  2-2-3    (8)      1, 2, 3, 4, 7, 8, 10, 12
•  2-2-4    (9)      1, 3, 4, 5, 6, 8, 10, 12, 16
•  2-2-5    (9)      1, 4, 5, 6, 8, 9, 12, 14, 20
•  2-2-6   (11)      1, 2, 4, 5, 6, 7, 8, 10, 14, 16, 24
•  2-3-3   (11)      1, 2, 3, 4, 7, 8, 9, 11, 12, 15, 18
•  2-3-4   (13)     1, 2, 3, 4, 5, 6, 9, 10, 11, 14, 18, 20, 24
•  2-3-5   (14)     1, 4, 5, 6, 7, 9, 10, 11, 13, 16, 17, 21, 25, 30
•  2-3-6   (14)     1, 4, 5, 6, 7, 9, 11, 12, 15, 16, 18, 20, 24, 30
•  2-4-4   (12)     1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 24
•  2-4-5   (14)     1, 2, 3, 6, 7, 10, 11, 12, 13, 14, 18, 22, 28, 30
•  2-4-6   (13)     1, 2, 3, 4, 5, 7, 8, 12, 14, 16, 20, 22, 26
•  2-5-5   (10)     1, 2, 3, 5, 8, 12, 15, 20, 23, 27
•  2-5-6   (15)     1, 2, 3, 4, 7, 8, 9, 13, 15, 16, 17, 18, 20, 22, 28
•  2-6-6    (9)     1, 2, 3, 6, 9, 10, 14, 18, 24
•  3-3-3    (8)     2, 3, 4, 6, 9, 12, 18, 27
•  3-3-4   (10)    2, 3, 4, 5, 9, 10, 13, 15, 21, 24
•  3-3-5   (10)     1, 4, 5, 6, 11, 12, 14, 18, 24, 30
•  3-3-6   (10)     1, 3, 5, 6, 7, 9, 12, 15, 21, 27
•  3-4-4   (11)     2, 3, 4, 5, 8, 11, 13, 16, 19, 24, 28
•  3-4-5   (13)     2, 3, 4, 5, 6, 7, 8, 11, 12, 17, 19, 23, 27
•  3-4-6   (14)     1, 2, 5, 6, 7, 8, 12, 13, 14, 18, 21, 22, 27, 30
•  3-5-5   (10)     2, 3, 4, 7, 10, 13, 20, 22, 28, 30
•  3-5-6   (14)     2, 3, 4, 7, 8, 9, 10, 12, 13, 14, 15, 21, 23, 27
•  3-6-6    (9)      2, 3, 4, 8, 9, 12, 15, 18, 24
•  4-4-4    (6)      2, 3, 4, 5, 12, 20
•  4-4-5    (9)      3, 4, 5, 6, 11, 13, 16, 21, 24
•  4-4-6   (10)     2, 5, 6, 7, 8, 10, 14, 20, 22, 28
•  4-5-5    (9)      3, 4, 5, 6, 14, 15, 21, 25, 29
•  4-5-6   (12)     2, 3, 4, 5, 6, 7, 10, 14, 15, 19, 26, 29
•  4-6-6    (9)      3, 4, 5, 8, 9, 12, 16, 18, 30
•  5-5-5    (7)       2, 4, 5, 6, 15, 20, 30
•  5-5-6    (7)      4, 5, 6, 7, 16, 19, 25
•  5-6-6    (6)      4, 5, 6, 7, 17, 24
•  6-6-6    (6)      2, 5, 6, 7, 18, 30

Mathematically Possible board game

To take yet another step forward, and to put all the above into practice, click Mathematically Possible for details of our popular board game that uses three numbers exactly like Roll3Dice, but involves strategy and decision-making as well as arithmetic calculations.