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

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The Twelve Pointed Star Game

Age 7 to 11 Challenge Level:

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.