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I hope you enjoyed tackling this problem - a bit of a teaser! Many of you spotted that it is impossible to make 37 from ten odd numbers. Adam and Ryan from Moorfield Junior School wrote:

This problem is not possible because with an even number of odd numbers you cannot make an odd number. You can make 36 and 38 using 10 numbers but not 37. You can make 37, but by using 9 numbers. Here are some examples:

36 (10 numbers): 5 + 5 + 5 + 5 + 5 + 3 + 3 + 3 + 1 + 1
38 (10 numbers): 1 + 1 + 1 + 3 + 3 + 5 + 5 + 5 + 7 + 7
37 (9 numbers): 5 + 5 + 5 + 5 + 5 + 5 + 5 + 1 + 1

Alice from Tattingstone School sent a similar explanation and demonstrated other ways of making 37 with nine, eleven and thirteen numbers:

37 (9 numbers): 5 + 5 + 5 + 5 + 5 + 5 + 3 + 3 + 1
37 (9 numbers): 5 + 5 + 5 + 5 + 5 + 7 + 1 + 1 + 3
37 (11 numbers): 5 + 5 + 5 + 5 + 5 + 3 + 3 + 3 + 1 + 1 + 1
37 (13 numbers): 7 + 7 + 7 + 7 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

Joshua from Tattingstone School explained very clearly why the problem was impossible:

I looked at the numbers in the bag and discovered that they were all odd. I know that it is a mathematical fact that if you take any two odd numbers and add them together, you will always get an even number as the answer e.g. 9 + 7 = 16. Therefore any even combination of odd numbers will also always give an even number as the answer e.g. 7 + 1 + 5 + 9 = 22. The question asks me to make 37, which is an odd number, out of 10 odd numbers which due to the facts above is impossible.

Joanna from Tattingstone suggested more ways of making 36 or 38 using ten numbers and mentioned that she could make 37 with seven, nine, eleven etc numbers. Interestingly, Joanna pointed out that you couldn't make 37 using five of the numbers because 7 is the biggest number you could use and 5 x 7 = 35 which is no good.

Alistair who goes to Histon and Impington Junior School looked at it in a slightly different way:

You can make 37 using a combination of 9 numbers, but to use 10 numbers, you need to split one of the 9 numbers into two others (that are in the bags).
Since all these numbers are odd, it is impossible to split them up into exactly two whole numbers from other bags.

Aryeh and Gitty from Bournemouth Jewish Day School found it was impossible and suggested that you could do it if you could multiply then add or subtract:

5 x 5 + 5 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 37
5 x 5 + 3 + 1+ 1 + 3 +1 + 1 + 1 + 1 = 37
5 x 7 + 1 + 1 + 1 + 1 - 1 - 1 - 1 + 1 =37

Julie from Hillside Community Primary School also noticed that if multiplying were allowed, it would have worked:

1 x 1 x 1 x 1 x 1 x 1 x 5 x 7 + 5 - 3 = 37

Well done also to all these people who noticed that you couldn't make 37 in this way:

  • Charlotte and Lauren from Hillside Community Primary School
  • Helen, Katie, Pauline, Ryo and Jake from Moorfield Junior School
  • Deep, Chad, Henri, and Olof at the Canadian Academy in Kobe, Japan
  • Pupils at Balgowan Primary School