Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read I've submitted a solution  what next?
Over the summer break, instead of live problems, we are offering a selection of Maths at Home challenges, which are ideal for working on with friends or relatives. We hope you enjoy thinking mathematically at home.
Live problems

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Quadratic Patterns
Surprising numerical patterns can be explained using algebra and diagrams...

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Picturing Square Numbers
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Recently solved problems

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Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Slick Summing
Watch the video to see how Charlie works out the sum. Can you adapt his method?

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Cyclic Quadrilaterals
Draw some quadrilaterals on a 9point circle and work out the angles. Is there a theorem?

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Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Cuboid Challenge
What's the largest volume of box you can make from a square of paper?

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Take Three From Five
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?

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M, M and M
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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Have you got it?
Can you explain the strategy for winning this game with any target? 

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Wipeout
Can you do a little mathematical detective work to figure out which number has been wiped out? 
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Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.