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# The Twelve Pointed Star Game

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### Exploring Wild & Wonderful Number Patterns

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Age 7 to 11

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Congratulations to Cong Lu from Aberdeen , Keshav from Singapore, Fionne from Leiston, George from St Nicholas C of E Junior School and Luke from Wirral Grammar School for Boys who all sent in correct solutions.

George's solution is given below:

We all played the game in pairs and then looked at which were the winning numbers.

The best numbers (the numbers that won the most times) were 6, 7, 8, 9 and 10.

I made a list of the different combinations of scores on the
dice making each number:

1~~~~ not possible

2~~~~1,1

3~~~~1,2~~2,1

4~~~~1,3~~2,2~~3,1

5~~~~1,4~~2,3~~3,2~~4,1

6~~~~1,5~~2,4~~3,3~~4,2~~5,1

7~~~~1,6~~2,5~~3,4~~4,3~~5,2~~6,1

8~~~~2,6~~3,5~~4,4~~5,3~~6,2

9~~~~3,6~~4,5~~5,4~~6,3

10~~4,6~~5,5~~6,4

11~~5,6~~6,5

12~~6,6

The best numbers to choose are 6, 7 and 8 because they have the most combinations.

When we played this game, the worst numbers (the numbers which lost the most times) were 2, 3, 4, 5, 11 and 12. These are poor numbers to choose because they don't have many combinations.

The worst number to choose is 1 because it doesn't have any
combinations.

These two group activities use mathematical reasoning - one is numerical, one geometric.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.