Secondary Interactive Summer Challenges 2022

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.

game

Phiddlywinks

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

problem

Favourite

Beelines

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?

problem

Favourite

Nine Colours

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?

problem

Favourite

Frogs

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?

problem

Favourite

Tilted Squares

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?

problem

3D Treasure Hunt

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?

problem

Favourite

Isosceles Triangles

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?

problem

Favourite

Stars

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?

problem

Favourite

The Better Choice

Age

14 to 16

Challenge level

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

problem

Favourite

Magic potting sheds

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?

problem

Favourite

Connect Three

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?

problem

crossing the bridge

Age

11 to 18

Challenge level

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

problem

Favourite

In the bag

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?

problem

L-triominoes

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?

problem

Favourite

Finding factors

Age

14 to 16

Challenge level

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

problem

Comparing Carbon Footprints

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.

problem

Favourite

Fruity Totals

Age

7 to 16

Challenge level

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

problem

Favourite

Number Lines in Disguise

Age

7 to 14

Challenge level

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

problem

Favourite

Treasure Hunt

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?

problem

Favourite

Your number is...

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?

problem

Favourite

Remainders

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?

problem

Favourite

Dozens

Age

7 to 14

Challenge level

Can you select the missing digit(s) to find the largest multiple?

problem

Favourite

The Number Jumbler

Age

7 to 14

Challenge level

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

problem

Latin Lilies

Age

7 to 14

Challenge level

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

problem

Favourite

Charlie's delightful machine

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?

problem

Favourite

What numbers can we make now?

Age

11 to 14

Challenge level

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

problem

Favourite

Square coordinates

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?