Reasoning, convincing and proving

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

problem

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Special numbers

Age

11 to 14

Challenge level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

problem

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Diagonal sums

Age

7 to 14

Challenge level

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

problem

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Squares in rectangles

Age

11 to 14

Challenge level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

problem

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Thousands and millions

Age

11 to 14

Challenge level

Here's a chance to work with large numbers...

problem

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Pairs of numbers

Age

5 to 7

Challenge level

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

problem

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Shape and territory

Age

16 to 18

Challenge level

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

problem

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2-digit square

Age

14 to 16

Challenge level

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

problem

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Sealed solution

Age

7 to 11

Challenge level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

problem

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Sixty-seven squared

Age

16 to 18

Challenge level

Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?

problem

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Product sudoku

Age

11 to 16

Challenge level

The clues for this Sudoku are the product of the numbers in adjacent squares.

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Reasoning, convincing and proving

Special numbers

Diagonal sums

Squares in rectangles

Thousands and millions

Pairs of numbers

Shape and territory

2-digit square

Sealed solution

Sixty-seven squared

Product sudoku