List

Being Resourceful - Secondary Students

Being Resourceful is part of our Developing Mathematical Habits of Mind collection.

Good thinkers are resourceful and reflective. They think critically and can explain and justify the choices that they make. They become absorbed in what they are doing and show attention to detail. They look back on what they have done in order to learn from both successes and failures.

Want to become more resourceful?

These problems may require careful consideration. Immerse yourself in them - we think they are worth the effort!

You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.
Quadrilaterals game
game
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Quadrilaterals game

A game for 2 or more people, based on the traditional card game Rummy.
Transformation Game
game
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Transformation Game

Why not challenge a friend to play this transformation game?
How old am I?
problem
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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?
Funny Factorisation
problem
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Funny Factorisation

Age
11 to 16
Challenge level
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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
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?
Marbles in a box
problem
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Marbles in a box

Age
11 to 16
Challenge level
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How many winning lines can you make in a three-dimensional version of noughts and crosses?
Attractive Tablecloths
problem
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Attractive Tablecloths

Age
14 to 16
Challenge level
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Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
In a box
problem
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In a box

Age
14 to 16
Challenge level
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Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?
Heads and Feet
problem
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Heads and Feet

Age
5 to 7
Challenge level
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On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
Twenty Divided into Six
problem
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Twenty Divided into Six

Age
7 to 11
Challenge level
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Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Triangles to Tetrahedra
problem
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Triangles to Tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Sealed Solution
problem
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Sealed Solution

Age
7 to 11
Challenge level
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Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Frogs
problem
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Frogs

Age
11 to 14
Challenge level
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How many moves does it take to swap over some red and blue frogs? Do you have a method?
Shady Symmetry
problem
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Shady Symmetry

Age
11 to 14
Challenge level
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How many different symmetrical shapes can you make by shading triangles or squares?
Hexy-Metry
problem
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Hexy-Metry

Age
14 to 16
Challenge level
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A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Eggs in Baskets
problem
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Eggs in Baskets

Age
5 to 7
Challenge level
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There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?
The Tall Tower
problem
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The Tall Tower

Age
5 to 7
Challenge level
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As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
The Spider and the Fly
problem
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The Spider and the Fly

Age
14 to 16
Challenge level
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A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Cuboids
problem
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Cuboids

Age
11 to 14
Challenge level
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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
On the Edge
problem
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On the Edge

Age
11 to 14
Challenge level
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If you move the tiles around, can you make squares with different coloured edges?
Isosceles Triangles
problem
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Isosceles Triangles

Age
11 to 14
Challenge level
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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Odds and Evens
problem
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Odds and Evens

Age
11 to 14
Challenge level
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Are these games fair? How can you tell?
Two's company
problem
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Two's company

Age
11 to 14
Challenge level
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Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Cosy corner
problem
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Cosy corner

Age
11 to 14
Challenge level
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Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
Substitution Cipher
problem
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Substitution Cipher

Age
11 to 14
Challenge level
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Find the frequency distribution for ordinary English, and use it to help you crack the code.
Torn Shapes
problem
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Torn Shapes

Age
7 to 11
Challenge level
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These rectangles have been torn. How many squares did each one have inside it before it was ripped?
A Chance to Win?
problem
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A Chance to Win?

Age
11 to 14
Challenge level
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Imagine you were given the chance to win some money... and imagine you had nothing to lose...
Four Go
problem
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Four Go

Age
7 to 11
Challenge level
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This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
Shape Times Shape
problem
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Shape Times Shape

Age
7 to 11
Challenge level
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These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Difference Sudoku
problem
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Difference Sudoku

Age
14 to 16
Challenge level
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Use the differences to find the solution to this Sudoku.
Cows and Sheep
problem

Cows and Sheep

Age
7 to 11
Challenge level
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Use your logical reasoning to work out how many cows and how many sheep there are in each field.
Which spinners?
problem
Favourite

Which spinners?

Age
14 to 18
Challenge level
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Can you work out which spinners were used to generate the frequency charts?
Eight hidden squares
problem
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Eight hidden squares

Age
7 to 14
Challenge level
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On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Nice or Nasty
problem
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Nice or Nasty

Age
7 to 14
Challenge level
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There are nasty versions of this dice game but we'll start with the nice ones...
How much can we spend?
problem
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How much can we spend?

Age
11 to 14
Challenge level
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A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Tower of Hanoi
problem
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Tower of Hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Sociable Cards
problem
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Sociable Cards

Age
11 to 14
Challenge level
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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Last one standing
problem
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Last one standing

Age
14 to 16
Challenge level
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Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?
What does random look like?
problem
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What does random look like?

Age
11 to 14
Challenge level
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Engage in a little mathematical detective work to see if you can spot the fakes.
Finding factors
problem
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Finding factors

Age
14 to 16
Challenge level
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Can you find the hidden factors which multiply together to produce each quadratic expression?
Constructing Triangles
problem
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Constructing Triangles

Age
11 to 14
Challenge level
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Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Play to 37
problem
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Play to 37

Age
7 to 11
Challenge level
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In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Perception versus reality
problem
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Perception versus reality

Age
14 to 18
Challenge level
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Infographics are a powerful way of communicating statistical information. Can you come up with your own?
Wipeout
problem
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Wipeout

Age
11 to 16
Challenge level
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Can you do a little mathematical detective work to figure out which number has been wiped out?
Box plot match
problem
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Box plot match

Age
14 to 16
Challenge level
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Match the cumulative frequency curves with their corresponding box plots.
Cryptarithms
problem
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Cryptarithms

Age
11 to 14
Challenge level
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Can you crack these cryptarithms?
Forwards Add Backwards
problem
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Forwards Add Backwards

Age
11 to 14
Challenge level
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What happens when you add a three digit number to its reverse?
Reversals
problem
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Reversals

Age
11 to 14
Challenge level
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Where should you start, if you want to finish back where you started?
Unequal Averages
problem
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Unequal Averages

Age
11 to 14
Challenge level
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Play around with sets of five numbers and see what you can discover about different types of average...
Gabriel's Problem
problem
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Gabriel's Problem

Age
11 to 14
Challenge level
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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Satisfying Four Statements
problem
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Satisfying Four Statements

Age
7 to 11
Challenge level
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Can you find any two-digit numbers that satisfy all of these statements?
Number Lines in Disguise
problem
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Number Lines in Disguise

Age
7 to 14
Challenge level
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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Coded hundred square
problem
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Coded hundred square

Age
7 to 11
Challenge level
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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Treasure Hunt
problem
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Treasure Hunt

Age
7 to 14
Challenge level
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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
Repeating Patterns
problem
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Repeating Patterns

Age
5 to 7
Challenge level
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Try continuing these patterns made from triangles. Can you create your own repeating pattern?
First Connect Three
problem
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First Connect Three

Age
7 to 11
Challenge level
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Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
Turning Man
problem
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Turning Man

Age
5 to 7
Challenge level
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Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
Dozens
problem
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Dozens

Age
7 to 14
Challenge level
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Can you select the missing digit(s) to find the largest multiple?
4 Dom
problem
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4 Dom

Age
5 to 11
Challenge level
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Use these four dominoes to make a square that has the same number of dots on each side.
Mystery Matrix
problem
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Mystery Matrix

Age
7 to 11
Challenge level
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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Poly Plug Rectangles
problem
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Poly Plug Rectangles

Age
5 to 11
Challenge level
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The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
missing multipliers
problem
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Missing Multipliers

Age
7 to 14
Challenge level
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What is the smallest number of answers you need to reveal in order to work out the missing headers?
A little light thinking
problem
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A little light thinking

Age
14 to 16
Challenge level
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Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Shifting Times Tables
problem
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Shifting Times Tables

Age
11 to 14
Challenge level
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Can you find a way to identify times tables after they have been shifted up or down?

Multiplication arithmagons
problem
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Multiplication arithmagons

Age
14 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Arithmagons
problem
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Arithmagons

Age
11 to 16
Challenge level
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Can you find the values at the vertices when you know the values on the edges?

Dotty Six
problem
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Dotty Six

Age
5 to 11
Challenge level
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Dotty Six is a simple dice game that you can adapt in many ways.

m, m and m
problem
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M, M and M

Age
11 to 14
Challenge level
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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Shapely pairs
problem
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Shapely pairs

Age
11 to 14
Challenge level
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A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Agile Algebra
problem

Agile Algebra

Age
16 to 18
Challenge level
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Observe symmetries and engage the power of substitution to solve complicated equations.

Square It
problem
Favourite

Square It

Age
11 to 16
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Dicey Operations
game
Favourite

Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Semi-regular Tessellations
problem
Favourite

Semi-regular Tessellations

Age
11 to 16
Challenge level
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Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Two and Two
problem
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Two and Two

Age
7 to 16
Challenge level
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How many solutions can you find to this sum? Each of the different letters stands for a different number.

Wallpaper
problem
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Wallpaper

Age
5 to 7
Challenge level
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These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

The animals' sports day
problem
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The animals' sports day

Age
5 to 7
Challenge level
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One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

Through the Window
problem
Favourite

Through the Window

Age
7 to 11
Challenge level
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My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Ladybird Count
problem
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Ladybird Count

Age
5 to 7
Challenge level
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Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Property chart
problem
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Property chart

Age
11 to 14
Challenge level
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A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Product Sudoku
problem
Favourite

Product Sudoku

Age
11 to 16
Challenge level
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The clues for this Sudoku are the product of the numbers in adjacent squares.

The Remainders Game
game
Favourite

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Xavi's T-shirt
problem
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Xavi's T-shirt

Age
7 to 16
Challenge level
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How much can you read into a T-shirt?

Magic Vs
problem
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Magic Vs

Age
7 to 11
Challenge level
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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Charlie's delightful machine
problem
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Charlie's delightful machine

Age
11 to 16
Challenge level
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Special Numbers
problem
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Special Numbers

Age
11 to 14
Challenge level
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My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Cut Nets
problem
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Cut Nets

Age
7 to 11
Challenge level
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Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

A Puzzling Cube
problem
Favourite

A Puzzling Cube

Age
7 to 11
Challenge level
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Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Square Corners
problem
Favourite

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?

Baravelle
problem
Favourite

Baravelle

Age
7 to 16
Challenge level
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What can you see? What do you notice? What questions can you ask?

Sponge Sections
problem
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Sponge Sections

Age
7 to 11
Challenge level
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You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Which solids can we make?
problem
Favourite

Which solids can we make?

Age
11 to 14
Challenge level
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Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Seeing Squares
problem
Favourite

Seeing Squares

Age
5 to 11
Challenge level
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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.