Secret Number

We received many solutions to this problem - thank you to you all. Holly from Hermitage School sent a particularly well-explained one:

You know that the number on the addition question is 6 because of two things.
1. I know that 6 + 4 = 10, and 4 was the choosen number, so 6 is what you add on to make 10.
2. You can subtract 4 from 10 and see what the number is. That number is then the secret number, 10 - 4 = 6.

You know that the number on the multiplication question is 7 because of 2 things.
1. I know my 5 times tables and I went through them, {5x1=5,2x5=10,3x5=15,4x5=20,5x5=25,6x5=30,7x5=35}. When I got to 35 I figured out what you times it by.
2. Another way to do it is to do division. 35 divided by 5 is 7. Also if you find division hard you can do 5 jars and 35 sweets.

I think Holly means that you can think of division as sharing, for example sharing out 35 sweets between 5 jars. Benjy from St Mary Redcliffe Primary looked at the first addition game more generally. He said:

If I ask to add one to the secret number then I can get the number from the answer by taking away one.
If I ask to add one hunded to the secret number then I can get the secret number from the answer by taking away one hundred.

Well done, Benjy - you have got the idea. Charoo from Manor Farm Junior School summed it up by saying:

That is indeed one way of doing it, as Holly has shown. Thank you again to all of you who contacted us.