The Remainders Game
Age
7 to 14
Challenge level
If you haven't already seen Remainders, it would be worth trying that task before playing this game.
The computer will think of a number between 1 and 100. Can you work out what it is?
Choose a divisor and the computer will give you some information about the number.
The fewer divisions you require, the more points you get.
If you identify the number correctly after
1 or 2 divisions - you gain 12 points
3 divisions - you gain 11 points
3 divisions - you gain 11 points
4 divisions - you gain 9 points
5 divisions - you gain 6 points
6 divisions - you gain 3 points
7 or more divisions - you gain 1 point
If you guess wrongly you lose 15 points, even if your guess satisfies all the criteria.
How soon can you reach 100 points?
Challenge your friends to do better.
The modulator will help you play the game, but eventually, try to play the game without it.
Click on the purple cog to open the settings menu and change the level of the game:
In Level 1 the chosen number will be from 1 to 60 inclusive and you can divide by each of the numbers from 1 to 10.
In Level 2 (the default setting), the chosen number will be from 1 to 100 inclusive and you can divide by each of the numbers from 2 to 10.
In Level 3 the chosen number will be from 1 to 100 inclusive and you can only divide by a selection of the numbers from 1 to 10.
In Level 2 (the default setting), the chosen number will be from 1 to 100 inclusive and you can divide by each of the numbers from 2 to 10.
In Level 3 the chosen number will be from 1 to 100 inclusive and you can only divide by a selection of the numbers from 1 to 10.
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.
Please see the Teachers' Resources for Remainders which offer suggestions for how to introduce the ideas involved in this game.