Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving

problem

Favourite

Lcm sudoku

Age

14 to 16

Challenge level

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

problem

Favourite

Three dice

Age

7 to 11

Challenge level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

problem

Favourite

Curious number

Age

7 to 11

Challenge level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

problem

Favourite

Areas and ratios

Age

16 to 18

Challenge level

Do you have enough information to work out the area of the shaded quadrilateral?

problem

Favourite

Cosines rule

Age

14 to 16

Challenge level

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

problem

Favourite

Doesn't add up

Age

14 to 16

Challenge level

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

problem

Favourite

Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

problem

Favourite

Zig zag

Age

14 to 16

Challenge level

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

problem

Favourite

Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

problem

Favourite

Eyes down

Age

16 to 18

Challenge level

The symbol [ ] means 'the integer part of'. Can the numbers [2x]; 2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three different values?

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Reasoning, convincing and proving

Lcm sudoku

Three dice

Curious number

Areas and ratios

Cosines rule

Doesn't add up

Differences

Zig zag

Think of two numbers

Eyes down