Solved: My Son Went To A Maths Master-Class Today...

While he was there he was set this problem:

Write down six numbers [from 1 to 9]

Starting from the left add consecutive numbers together in pairs. If the result is bigger than nine record the right-most digit.

Continue to do this until there are no more numbers to add together.

Record the last number when the addition is complete.

A worked example:

Starting numbers:

1, 2, 3, 4, 5, 6

1st stage:

3, 5, 7, 9, 1

2nd stage:

8, 2, 6, 0

3rd stage:

0, 8, 4

4th stage:

8, 4

5th stage:

2

Another worked example [for clarity]

Starting numbers:

4, 7, 9, 8, 2, 1

1st stage:

1, 6, 7, 0, 3

2nd stage:

7, 3, 7, 3

3rd stage:

0, 0, 0,

4th stage:

0, 0

5th stage:

0

The problem: Be able to predict the answer [at the 5th stage] without having to go through the stages in between.

The tutor called this 'Modular Maths' and he said that when you see the solution it is very simple. I can't see the pattern at the moment ['A' level maths is a long time ago for me. However my son is 11!]

Does anyone know how to explain this before it drives me crazy?

Thanks.