You may also like

problem icon

Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

problem icon

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

problem icon

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

The Remainders Game

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

If you guess wrong you lose 5 points, even if your guess satisfies the criteria, 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 $5$, as in the example below:


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.


Each division you carry out must provide new information - it must rule out some numbers. If you carry out unnecessary divisions you gain 0 points, even if your eventual guess is correct.

Suppose you are in the situation below, where 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, so you would score no points.