List

Secondary Interactive Summer Challenges 2022

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

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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.

 

Phiddlywinks
game

Phiddlywinks

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

Beelines

Age
14 to 16
Challenge level
filled star empty star empty star
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Nine Colours
problem
Favourite

Nine colours

Age
11 to 16
Challenge level
filled star filled star filled star
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?
Frogs
problem
Favourite

Frogs

Age
11 to 14
Challenge level
filled star empty star empty star
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Isosceles Triangles
problem
Favourite

Isosceles triangles

Age
11 to 14
Challenge level
filled star empty star empty star
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
Favourite

Stars

Age
11 to 14
Challenge level
filled star filled star empty star
Can you work out what step size to take to ensure you visit all the dots on the circle?
The Better Choice
problem
Favourite

The better choice

Age
14 to 16
Challenge level
filled star empty star empty star
Here are two games you can play. Which offers the better chance of winning?
Magic potting sheds
problem
Favourite

Magic potting sheds

Age
11 to 16
Challenge level
filled star filled star empty star
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?
In the bag
problem
Favourite

In the bag

Age
11 to 14
Challenge level
filled star empty star empty star
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?
L-triominoes
problem

L-triominoes

Age
14 to 16
Challenge level
filled star filled star empty star
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
Finding factors
problem
Favourite

Finding factors

Age
14 to 16
Challenge level
filled star empty star empty star
Can you find the hidden factors which multiply together to produce each quadratic expression?
Comparing Carbon Footprints
problem

Comparing carbon footprints

Age
11 to 18
Challenge level
filled star empty star empty star
This interactivity is designed to help you gain a better understanding of how your lifestyle choices can affect your carbon footprint.
Number Lines in Disguise
problem
Favourite

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?
Your number is...
problem
Favourite

Your number is...

Age
7 to 14
Challenge level
filled star empty star empty star
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Latin Lilies
problem

Latin lilies

Age
7 to 14
Challenge level
filled star empty star empty star
In this game you are challenged to gain more columns of lily pads than your opponent.
Factors and Multiples Game
game
Favourite

Factors and multiples game

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

Countdown
game
Favourite

Countdown

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

Polygon Rings
problem
Favourite

Polygon rings

Age
11 to 14
Challenge level
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Join pentagons together edge to edge. Will they form a ring?

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?

Got It
problem
Favourite

Got it

Age
7 to 14
Challenge level
filled star filled star empty star

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.

Take Three From Five
problem
Favourite

Take three from five

Age
11 to 16
Challenge level
filled star filled star empty star

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?

The Remainders Game
game
Favourite

The remainders game

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

Diamond Collector
game
Favourite

Diamond collector

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

Last Biscuit
game

Last biscuit

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

Tilted Squares
problem
Favourite

Tilted squares

Age
11 to 14
Challenge level
filled star empty star empty star

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

What numbers can we make now?
problem
Favourite

What numbers can we make now?

Age
11 to 14
Challenge level
filled star filled star empty star

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

Charlie's delightful machine
problem
Favourite

Charlie's delightful machine

Age
11 to 16
Challenge level
filled star empty star empty star

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

crossing the bridge
problem

Crossing the bridge

Age
11 to 18
Challenge level
filled star filled star empty star

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

Connect Three
problem
Favourite

Connect three

Age
11 to 16
Challenge level
filled star filled star empty star

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

Dozens
problem
Favourite

Dozens

Age
7 to 14
Challenge level
filled star empty star empty star

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

Remainders
problem
Favourite

Remainders

Age
7 to 14
Challenge level
filled star filled star empty star

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

3D Treasure Hunt
problem

3D treasure hunt

Age
14 to 18
Challenge level
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Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

The Number Jumbler
problem
Favourite

The Number Jumbler

Age
7 to 14
Challenge level
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The Number Jumbler can always work out your chosen symbol. Can you work out how?

Treasure Hunt
problem
Favourite

Treasure hunt

Age
7 to 14
Challenge level
filled star empty star empty star

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

Fruity Totals
problem
Favourite

Fruity totals

Age
7 to 16
Challenge level
filled star empty star empty star

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

Square coordinates
problem
Favourite

Square coordinates

Age
11 to 14
Challenge level
filled star filled star empty star

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?

Square It
problem
Favourite

Square it

Age
11 to 16
Challenge level
filled star empty star empty star

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.