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.

What Numbers Can We Make Now?

Age 11 to 14Challenge Level

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

Remainders

Age 7 to 14Challenge 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?

The Remainders Game

Age 7 to 14Challenge Level

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

Polygon Rings

Age 11 to 14Challenge Level

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

L-triominoes

Age 14 to 16Challenge Level

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

Latin Lilies

Age 7 to 14Challenge Level

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

Diamond Collector

Age 11 to 16Challenge Level

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

Dozens

Age 7 to 14Challenge Level

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

Stars

Age 11 to 14Challenge Level

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

Take Three from Five

Age 11 to 16Challenge 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?

Phiddlywinks

Age 7 to 18Challenge Level

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

In the Bag

Age 11 to 14Challenge 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?

Tilted Squares

Age 11 to 14Challenge Level

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

Semi-regular Tessellations

Age 11 to 16Challenge Level

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

Countdown

Age 7 to 14Challenge Level

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

The Better Choice

Age 14 to 16Challenge Level

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

Last Biscuit

Age 11 to 18Challenge Level

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

Factors and Multiples Game

Age 7 to 16Challenge Level

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

Magic Potting Sheds

Age 11 to 16Challenge 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?

Number Lines in Disguise

Age 7 to 14Challenge Level

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

Estimating Angles

Age 7 to 14Challenge Level

How good are you at estimating angles?

3D Treasure Hunt

Age 14 to 18Challenge Level

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

Treasure Hunt

Age 7 to 14Challenge Level

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

Beelines

Age 14 to 16Challenge Level

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

Nine Colours

Age 11 to 16Challenge 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 14Challenge Level

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

Square Coordinates

Age 11 to 14Challenge 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?

Charlie's Delightful Machine

Age 11 to 16Challenge Level

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

Isosceles Triangleslive

Age 11 to 14Challenge 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?

Got It

Age 7 to 14Challenge 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.

Finding Factors

Age 14 to 16Challenge Level

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

Fruity Totals

Age 7 to 16Challenge Level

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

Connect Three

Age 11 to 16Challenge Level

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

Frogs

Age 11 to 14Challenge Level

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

The Number Jumbler

Age 7 to 14Challenge Level

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

Square It

Age 11 to 16Challenge 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.

Crossing the Bridge

Age 11 to 18Challenge Level

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