Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Filling the gaps
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Filling the gaps

Age
14 to 16
Challenge level
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Which numbers can we write as a sum of square numbers?
Can they be equal?
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Can they be equal?

Age
11 to 14
Challenge level
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Can you find rectangles where the value of the area is the same as the value of the perimeter?
Generating Triples
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Generating triples

Age
14 to 16
Challenge level
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Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
Number Pyramids
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Number pyramids

Age
11 to 14
Challenge level
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Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Odds, Evens and More Evens
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Odds, evens and more evens

Age
11 to 14
Challenge level
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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Round and round the circle
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Round and round the circle

Age
7 to 11
Challenge level
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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Have you got it?
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Have you got it?

Age
11 to 14
Challenge level
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Can you explain the strategy for winning this game with any target?
Two Primes Make One Square
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Two primes make one square

Age
7 to 11
Challenge level
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Can you make square numbers by adding two prime numbers together?
Mind Reading
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Mind reading

Age
11 to 14
Challenge level
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Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I know?
Break it up!
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Break it up!

Age
5 to 11
Challenge level
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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?