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The Remainders Game

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

This game follows on from Remainders

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 guess correctly after
2 divisions - you gain 10 points
3 divisions - you gain 9 points
4 divisions - you gain 8 points
5 divisions - you gain 7 points
6 divisions - you gain 6 points
7 divisions - you gain 5 points
8 divisions - you gain 4 points
9 divisions - you gain 3 points

If you guess wrong you lose 5 points, even if your guess satisfies the criteria.

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 guess is correct.
e.g. You will score no points if you divide by 2 after dividing by 4, since it will provide no new information (dividing by 4 will already have told you if the number you are looking for is even or odd).

How soon can you reach 100 points?
Challenge your friends to do better.

Full Screen Version
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You can use the interactivity below to help you play the game, but eventually, try to play the game without the aid of the interactivity.

You can print this 10 by 10 grid  and use it to help you keep a record of your working as you narrow down the possibilities.

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