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The Twelve Pointed Star Game

Age 7 to 11
Challenge Level Yellow starYellow star
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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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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