Which of the cities shown had the largest percentage increase in population?

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Weekly Problem 36 - 2008

Weighing the baby at the clinic was a problem. The baby would not keep still so we had to hold her while on the scales. Can you work out our combined weight?

Can you make a hypothesis to explain these ancient numbers?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

Weekly Problem 48 - 2013

What is the remainder when the number 743589×301647 is divided by 5?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. One day four of these creatures, two Zios and two Zepts, sat on the summit of a hill to count the legs of. . . .

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

If two friends run in opposite directions around a track, and they pass each other every 24 seconds, how long do they take to complete a lap?

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?

Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

How many visitors does a tourist attraction need next week in order to break even?

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

If a ball is rolled into the corner of a room how far is its centre from the corner?

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

What can you see? What do you notice? What questions can you ask?

Weekly Problem 11 - 2013

A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

This investigation is about happy numbers in the World of the Octopus where all numbers are written in base 8 .Octi the octopus counts.

Explore a number pattern which has the same symmetries in different bases.

The number 3723(in base 10) is written as 123 in another base. What is that base?

Two students collected some data on the wingspan of bats, but each lost a measurement. Can you find the missing information?

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

Can you figure out how sequences of beach huts are generated?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

A preview of some of the beam deflection mechanics you will look at in the first year of an engineering degree

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

This article explains the use of the idea of connectedness in networks, in two different ways, to bring into focus the basics of the game of Go, namely capture and territory.