Good thinkers are curious and ask good questions. They are excited by new ideas and are keen to explore and investigate them.
Want to become a more curious mathematician?
We hope these problems will provoke you to ask good mathematical questions. Take a look, we think you'll get hooked on them!
You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.
If the World Were a Village
This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?
Five Steps to 50
Next-door Numbers
Eightness of Eight
Digit Addition
Try out this number trick. What happens with different starting numbers? What do you notice?
Shaping It
Ring a Ring of Numbers
Colouring Triangles
Chain of Changes
Little Man
Light the Lights
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
More Numbers in the Ring
Consecutive Numbers
Number Differences
Brush Loads
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Statement Snap
Tumbling Down
Watch this animation. What do you see? Can you explain why this happens?
Fruity Totals
The Number Jumbler
Nice or Nasty
Your number is...
Three neighbours
Two Clocks
These clocks have only one hand, but can you work out what time they are showing from the information?
Pouring Problem
What do you think is going to happen in this video clip? Are you surprised?
Curious number
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Summing Consecutive Numbers
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Perimeter Possibilities
Semi-regular Tessellations
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Blue and White
Satisfying Statements
What's it worth?
Elevenses
Can they be equal?
Your number was...
Special Numbers
Number Pyramids
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
How much can we spend?
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
Tilted Squares
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?
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Dicey Operations
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Arithmagons
Can you find the values at the vertices when you know the values on the edges?
Non-Transitive Dice
Right angles
What numbers can we make now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Two's company
Cosy corner
Estimating time
Wipeout
Unequal Averages
Marbles in a box
Think of Two Numbers
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?
Searching for mean(ing)
Cuboid Challenge
What's the largest volume of box you can make from a square of paper?
More Number Pyramids
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
On the Edge
Sending a Parcel
Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Square coordinates
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Stars
Litov's Mean Value Theorem
A Chance to Win?
Cola Can
Which solids can we make?
How old am I?
Beelines
Which spinners?
Curvy areas
Pair Products
Circles in quadrilaterals
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Last one standing
A little light thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Vector journeys
Triangle midpoints
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Odds and Evens made fair
What's Possible?
Arclets
Trapezium Four
Pick's Theorem
Triangles and petals
Same Number!
Partly Painted Cube
Where to Land
Multiplication arithmagons
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?