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## 'Pairs of Numbers' printed from http://nrich.maths.org/

We had three good solutions sent in for this challenge. They explained their answers clearly. Well done!

Jacob and Michael from Cloverdale Catholic School in Canada wrote:
Because there are ten counters there are only four matches. (1+9, 6+4, 3+7, 2+8).

Apparently, there is only one five so 5+5 is not possible.

There is no zero so 0+10 is not possible.

If there are eleven counters, there are five possible matches. (1+10, 2+9, 3+8, 4+7, 5+6).

Benjamin from West Oxford Primary School wrote:

Pairs that make 10 are 1+9, 2+8, 3+7, 4+6

Eight counters were used. Counters 10 and 5 were not used.

Pairs that make 12 are 2+10, 3+9, 4+8, 5+7

Eight counters were used. Counters 1 and 6 were not used.

Pairs that make 13 are 3+10, 4+ 9, 5+8, 6+7

Eight counters were used. Counters 1 and 2 were not used.

Pairs that make 11 are 1+10, 2+9, 3+8, 4+7, 5+6

Ten counters were used. All counters were used.

Casper from Torbay Primary School in New Zealand sent in the following:

1. The pairs 9-1, 8-2, 7-3, 6-4 work

That leaves 10 and 5, 10 because 10+0 is ten but there is no zero and 5 because double 5 is ten but there is only one 5.

2. The pairs 10-2, 9-3, 8-4, 7-5 work

That leaves 1 and 6, 6 because double six is 12 but there is only one six and 1 because 1+11 is twelve but there is no eleven.

3. The pairs 10-3, 9-4, 8-5, 7-6 work

That leaves 1 and 2, 1 because 1+12 is thirteen but there is no twelve and 2 because 2+11 is thirteen but there is no eleven

4. The pairs 10-1, 9-2, 8-3, 7-4, 6-5 work

That leaves none so they all can be paired.