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There are **92** NRICH Mathematical resources connected to **Being resourceful**, you may find related items under Developing positive attitudes.

Problem
Primary curriculum
Secondary curriculum
### First Connect Three

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Difference Sudoku

Use the differences to find the solution to this Sudoku.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Go

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Chance to Win?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Turning Man

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Age 5 to 7

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Transformation Game

Why not challenge a friend to play this transformation game?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Wallpaper

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

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Torn Shapes

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Substitution Cipher

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Product Sudoku

The clues for this Sudoku are the product of the numbers in adjacent squares.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cosy Corner

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two's Company

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Property Chart

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shapely Pairs

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...

Age 11 to 14

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Quadrilaterals Game

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arithmagons

Can you find the values at the vertices when you know the values on the edges?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Stars

Can you work out what step size to take to ensure you visit all the dots on the circle?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Isosceles Triangles

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square It

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.

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### On the Edge

If you move the tiles around, can you make squares with different coloured edges?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuboids

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Spider and the Fly

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Tall Tower

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladybird Count

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cut Nets

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sponge Sections

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Special Numbers

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Eggs in Baskets

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hexy-metry

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shady Symmetry

How many different symmetrical shapes can you make by shading triangles or squares?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Frogs

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sealed Solution

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles to Tetrahedra

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Corners

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Puzzling Cube

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mystery Matrix

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Twenty Divided Into Six

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Heads and Feet

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Box

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Attractive Tablecloths

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Marbles in a Box

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two and Two

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where Can We Visit?

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Funny Factorisation

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Old Am I?

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 4 Dom

Use these four dominoes to make a square that has the same number of dots on each side.

Age 5 to 11

Challenge Level