Thank you to those of you who submitted comments about this game.

Anika from Holy Family Catholic Primary School in Boothstown, Manchester suggested the following rules:

- The answer from the previous calculation should be the answer to the next one
- You can only use each number once
- Player A uses addition and Player B uses subtraction, and this pattern follows throughout the game
- The aim of the game is to stop the other player from getting a calculation from the remaining numbers

Thank you, Anika! Jake said:

- Player A does a calculation using numbers 0-20. They cross off the numbers they use but circle the answer.
- Player B then uses the answer of player A’s calculation to start their number sentence.
- Each player can decide whether they would like to add or subtract.
- The player who cannot make a calculation from the numbers remaining loses the game.

So, it seems that Anika and Jake were largely in agreement. Anika, it does look like the order of calculations goes addition, subtraction, addition, subtraction etc from what we see in the video, you're right. However, I would suggest that the order doesn't matter. (You can read our suggested rules by clicking on the 'Show' button underneath the video on the problem page itself.)

Eleanor from Cottenham Primary School told us:

Good ways to win are to try and use up the numbers 1, 2, 3, 4 and possibly 5 and 6, because you can get to many different numbers by adding those whereas with the larger numbers you cannot get to so many because you can only go up to the number 20.

Eleanor also went on to explore the cooperative challenges. She says:

We can’t use all of the numbers because:

For the number line going from 0 to 20, you cannot use zero as you wouldn’t be adding or taking away anything so you would stay on the same number.

Yes, Eleanor, if you add zero, or take away zero, from a number, the answer to your calculation is the same number, so you would need to be able to use a number more than once and the rules don't allow this.

For the number line going from 1 to 20, you cannot use all the numbers because there will always be one number left over.

Each new calculation uses two new numbers apart from the first calculation which uses three so if you keep adding two to three you will always be on odd numbers and 20 is an even number, not odd.

Thank you, Eleanor, what great reasoning. Can you follow Eleanor's argument?