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There are **96** NRICH Mathematical resources connected to **Being curious**, you may find related items under Developing positive attitudes.

Problem
Primary curriculum
Secondary curriculum
### Can They Be Equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Elevenses

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Searching for Mean(ing)

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Spinners?

Can you work out which spinners were used to generate the frequency charts?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cola Can

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Age 11 to 14

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
### Trapezium Four

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Litov's Mean Value Theorem

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Age 11 to 14

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
### Two Clocks

These clocks have only one hand, but can you work out what time they are showing from the information?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Little Man

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Age 5 to 7

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
### Right Angles

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Differences

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Numbers in the Ring

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ring a Ring of Numbers

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Age 5 to 7

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
### 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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where to Land

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sending a Parcel

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Age 11 to 14

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
### Tilted Squares

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Your Number Is...

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Number Pyramids

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Pyramids

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pair Products

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

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
### Triangles and Petals

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Three by One

There are many different methods to solve this geometrical problem - how many can you find?

Age 16 to 18

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
### Pick's Theorem

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Largest Product

Which set of numbers that add to 100 have the largest product?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Think of Two Numbers

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's it Worth?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Age 11 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
### Arclets

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Blue and White

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's Possible?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Beelines

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

Age 14 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
### 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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle Midpoints

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Colouring Triangles

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Age 7 to 14

Challenge Level