Conjecturing and generalising

There are 405 NRICH Mathematical resources connected to Conjecturing and generalising
Carroll Diagrams
problem
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Carroll diagrams

Age
5 to 11
Challenge level
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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Sweets in a box
problem
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Sweets in a box

Age
7 to 11
Challenge level
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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

How old am I?
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How old am i?

Age
14 to 16
Challenge level
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In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Where can we visit?
problem
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Where can we visit?

Age
11 to 14
Challenge level
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Square Corners
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Square corners

Age
7 to 11
Challenge level
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What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Up and Down Staircases
problem
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Up and down staircases

Age
7 to 11
Challenge level
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One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
Stars
problem
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Stars

Age
11 to 14
Challenge level
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Can you work out what step size to take to ensure you visit all the dots on the circle?
Mixing More Paints
problem
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Mixing more paints

Age
14 to 16
Challenge level
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Can you find an efficent way to mix paints in any ratio?
Music to my Ears
problem
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Music to my ears

Age
7 to 11
Challenge level
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Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
Stop the Clock
problem
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Stop the clock

Age
5 to 7
Challenge level
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This is a game for two players. Can you find out how to be the first to get to 12 o'clock?