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Baby Boom

Age 14 to 16 Short Challenge Level:

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

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Baby Circle

Age 16 to 18 Challenge Level:

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?

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Baby's Weight

Age 11 to 14 Short Challenge Level:

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?

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Babylon Numbers

Age 11 to 18 Challenge Level:

Can you make a hypothesis to explain these ancient numbers?

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Back Fitter

Age 14 to 16 Challenge Level:

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?

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Back in Time

Age 14 to 16 Short Challenge Level:

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

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Back of the Queue

Age 11 to 14 Short Challenge Level:

Weekly Problem 48 - 2013
What is the remainder when the number 743589×301647 is divided by 5?

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Back to Basics

Age 14 to 16 Challenge Level:

Find b where 3723(base 10) = 123(base b).

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Back to School

Age 7 to 11 Challenge Level:

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?

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Back to the Planet of Vuvv

Age 11 to 14 Challenge Level:

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. . . .

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Back to the Practical?

Age 7 to 14

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. . . .

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Backwards Laps

Age 14 to 16 Short Challenge Level:

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?

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Baked Bean Cans

Age 5 to 7 Challenge Level:

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

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Balance of Halves

Age 7 to 11 Challenge Level:

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?

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Balance Point

Age 14 to 16 Challenge Level:

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?

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Balance Power

Age 11 to 18 Challenge Level:

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?

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Balances

Age 3 to 5

Put some objects on the balance scales. What do you notice?

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Balances and Springs

Age 14 to 16 Challenge Level:

Balancing interactivity with springs and weights.

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Balancing 1

Age 11 to 14 Challenge Level:

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.

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Balancing 2

Age 11 to 14 Challenge Level:

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.

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Balancing 3

Age 11 to 14 Challenge Level:

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.

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Balancing Act

Age 3 to 7 Challenge Level:

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Balancing the Books

Age 11 to 14 Short Challenge Level:

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

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Ball Bearings

Age 16 to 18 Challenge Level:

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.

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Ball Packing

Age 14 to 16 Challenge Level:

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

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Bands and Bridges: Bringing Topology Back

Age 7 to 14

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

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Baravelle

Age 7 to 16 Challenge Level:

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

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Bargain

Age 14 to 16 Short Challenge Level:

Weekly Problem 11 - 2013
A shop has "Everything half price", and then "15% off sale prices". What is the overall reduction in cost?

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Base Puzzle

Age 11 to 14 Challenge Level:

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

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Basic Rhythms

Age 16 to 18 Challenge Level:

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

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Basically

Age 11 to 14 Challenge Level:

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

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Baskets

Age 3 to 5

Counting reliably Solving problems, including doubling, halving and sharing.

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Bat and Ball

Age 14 to 16 Short Challenge Level:

Can you work out how much this bat costs?

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Bat Wings

Age 11 to 14 Short Challenge Level:

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

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Bateaux Sur Lac

Age 14 to 16 Challenge Level:

"Speeding Boats" en Français

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Battery Modelling

Age 16 to 18 Challenge Level:

Find out how to model a battery mathematically

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BCME 2014

Resources to accompany Charlie's presentations at BCME 2014.

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Be Reasonable

Age 16 to 18 Challenge Level:

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

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Beach Huts

Age 11 to 14 Challenge Level:

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

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Beads

Age 7 to 11 Challenge Level:

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

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Beads and Bags

Age 5 to 11 Challenge Level:

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?

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Beam Me Up

Age 16 to 18 Challenge Level:

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

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Bean Bags for Bernard's Bag

Age 7 to 11 Challenge Level:

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?

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Beat the Drum Beat!

Age 7 to 11 Challenge Level:

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

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Becky's Number Plumber

Age 7 to 11 Challenge Level:

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?

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Become Maths Detectives

Age 7 to 11 Challenge Level:

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.

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Beelines

Age 14 to 16 Challenge Level:

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

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Behind the Rules of Go

Age 14 to 18

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.