Reasoning, convincing and proving

There are 514 NRICH Mathematical resources connected to Reasoning, convincing and proving
Odds and Evens
problem
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Odds and evens

Age
11 to 14
Challenge level
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Are these games fair? How can you tell?
Times of Day
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Times of day

Age
5 to 7
Challenge level
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These pictures show some different activities that you may get up to during a day. What order would you do them in?

Dicey Addition
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Dicey addition

Age
5 to 11
Challenge level
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Who said that adding couldn't be fun?
Common Divisor
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Common divisor

Age
14 to 16
Challenge level
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Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
Iff
problem
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Iff

Age
14 to 18
Challenge level
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Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Take Three From Five
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Take three from five

Age
11 to 16
Challenge level
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Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Harmonic Triangle
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Harmonic triangle

Age
14 to 16
Challenge level
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Can you see how to build a harmonic triangle? Can you work out the next two rows?
Triangle Numbers
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Triangle numbers

Age
11 to 14
Challenge level
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Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
What Do you Need?
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What do you need?

Age
7 to 11
Challenge level
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Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Two-digit targets
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Two-digit targets

Age
5 to 7
Challenge level
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You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?