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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Secondary Interactive Summer Challenges 2022

### Last Biscuit

### Square It

### Take Three from Five

### Connect Three

### Got It

### Frogs

### Crossing the Bridge

### Factors and Multiples Game

### The Remainders Game

### What Numbers Can We Make Now?

### Remainders

### Polygon Rings

### Latin Lilies

### L-triominoes

### Diamond Collector

### Stars

### Phiddlywinks

### In the Bag

### Tilted SquaresLive

### Semi-regular Tessellations

### Countdown

### The Better Choice

### Comparing Carbon Footprints

### Magic Potting Sheds

### Number Lines in Disguise

### 3D Treasure Hunt

### Treasure Hunt

### Beelines

### Nine Colours

### Your Number Is...

### Square Coordinates

### Charlie's Delightful Machine

### Isosceles Triangles

### Finding Factors

### Fruity Totals

### The Number Jumbler

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

We have a challenge a day for you throughout the summer break...

Each weekday, from 18 July to 2 September, a new interactive game or puzzle will appear on this page.

After you've had a go at the day's challenge you may be able to compare your approach to the solutions we have published, which are based on students' work.

You can also find Primary Interactive Summer Challenges 2022.

Age 11 to 18

Challenge Level

Can you find a strategy that ensures you get to take the last biscuit in this game?

Age 11 to 16

Challenge Level

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

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

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

Age 7 to 14

Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Age 11 to 14

Challenge Level

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

Age 11 to 18

Challenge Level

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Age 7 to 16

Challenge Level

A game in which players take it in turns to choose a number. Can you block your opponent?

Age 7 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Age 7 to 14

Challenge Level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Age 11 to 14

Challenge Level

Join pentagons together edge to edge. Will they form a ring?

Age 7 to 14

Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

Age 14 to 16

Challenge Level

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Age 11 to 16

Challenge Level

Collect as many diamonds as you can by drawing three straight lines.

Age 11 to 14

Challenge Level

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

Age 7 to 18

Challenge Level

Have a go at this version of John Conway's game. Do you have any good strategies for winning?

Age 11 to 14

Challenge Level

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?

Age 11 to 14

Challenge Level

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

Age 11 to 16

Challenge Level

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

Age 7 to 14

Challenge Level

Here is a chance to play a version of the classic Countdown Game.

Age 14 to 16

Challenge Level

Here are two games you can play. Which offers the better chance of winning?

Age 11 to 18

Challenge Level

This interactivity is designed to help you gain a better understanding of how your lifestyle choices can affect your carbon footprint.

Age 11 to 16

Challenge Level

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Age 7 to 14

Challenge Level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Age 14 to 18

Challenge Level

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Age 7 to 14

Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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?

Age 11 to 16

Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Age 7 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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 16

Challenge Level

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

Age 11 to 14

Challenge Level

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 14 to 16

Challenge Level

Can you find the hidden factors which multiply together to produce each quadratic expression?

Age 7 to 16

Challenge Level

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Age 7 to 14

Challenge Level

The Number Jumbler can always work out your chosen symbol. Can you work out how?