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The Remainders Game

Age 7 to 14 Challenge Level:

This page contains some examples to clarify the rules for the Remainders Game.

If you guess wrong you lose 15 points, so don't guess until you are certain that there is only one possible answer.

Suppose you have discovered that your number has a remainder of $1$ when divided by $2$, and a remainder of $0$ when divided by $5$

At this point, you know that the hidden number is both odd and a multiple of $5$. You might think of $15$ as a number that would fit with both of these criteria.

However, there are still other possibilities that the number could be, such as $5$, $25$ or even $95$. This means that you'd need to do some more divisions to work out which number it is.

Try to ensure that each division you carry out provides new information - it should rule out some numbers. 

Suppose you have divided by $4$ and found that you are left with a remainder of $1$.

At this stage, you know your number is $1$ or $5$ or $9$ or..., so all the possibilities that you get are odd. Therefore, we already know that, if you choose to divide by $2$, the remainder will be $1$.

So, if you did divide by $2$ in this situation you would gain no extra information as to what the hidden number is.

If you carry out unnecessary divisions your score for getting the right answer will be lower.

You can use The Modulator tool to help you to decide whether a division will rule out any numbers.