List

Secondary Summer Challenges 2023

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

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Each weekday, from 10 July to 1 September, a new problem or game 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 Summer Challenges 2023.

 

What's Possible?
problem
Favourite

What's Possible?

Age
14 to 16
Challenge level
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Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Why 24?
problem
Favourite

Why 24?

Age
14 to 16
Challenge level
filled star filled star empty star
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Where can we visit?
problem
Favourite

Where can we visit?

Age
11 to 14
Challenge level
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
American Billions
problem
Favourite

American Billions

Age
11 to 14
Challenge level
filled star empty star empty star
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
Frogs
problem
Favourite

Frogs

Age
11 to 14
Challenge level
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How many moves does it take to swap over some red and blue frogs? Do you have a method?
Peaches today, Peaches tomorrow...
problem
Favourite

Peaches today, Peaches tomorrow...

Age
11 to 14
Challenge level
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A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Tourism
problem

Tourism

Age
11 to 14
Challenge level
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If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Consecutive Seven
problem
Favourite

Consecutive Seven

Age
11 to 14
Challenge level
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Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
Substitution Cipher
problem
Favourite

Substitution Cipher

Age
11 to 14
Challenge level
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Find the frequency distribution for ordinary English, and use it to help you crack the code.
Factors and Multiples Puzzle
problem
Favourite

Factors and Multiples Puzzle

Age
11 to 14
Challenge level
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?
Route to infinity
problem
Favourite

Route to infinity

Age
11 to 14
Challenge level
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Can you describe this route to infinity? Where will the arrows take you next?
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?
crossing the bridge
problem

crossing the bridge

Age
11 to 18
Challenge level
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Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Zin Obelisk
problem

Zin Obelisk

Age
11 to 14
Challenge level
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In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.
Multiples Sudoku
problem
Favourite

Multiples Sudoku

Age
11 to 14
Challenge level
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Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Sticky Numbers
problem
Favourite

Sticky Numbers

Age
11 to 14
Challenge level
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Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Always a multiple?
problem
Favourite

Always a multiple?

Age
11 to 14
Challenge level
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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Sociable Cards
problem
Favourite

Sociable Cards

Age
11 to 14
Challenge level
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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Magic Letters
problem
Favourite

Magic Letters

Age
11 to 14
Challenge level
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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Kite in a Square
problem
Favourite

Kite in a Square

Age
14 to 18
Challenge level
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Can you make sense of the three methods to work out what fraction of the total area is shaded?
Olympic Measures
problem
Favourite

Olympic Measures

Age
11 to 14
Challenge level
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These Olympic quantities have been jumbled up! Can you put them back together again?
Getting round the city
problem

Getting round the city

Age
11 to 16
In a city with a grid system of roads, how do you get from A to B?
Cryptarithms
problem
Favourite

Cryptarithms

Age
11 to 14
Challenge level
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Can you crack these cryptarithms?
Add to 200
problem
Favourite

Add to 200

Age
11 to 14
Challenge level
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By selecting digits for an addition grid, what targets can you make?
Forwards Add Backwards
problem
Favourite

Forwards Add Backwards

Age
11 to 14
Challenge level
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What happens when you add a three digit number to its reverse?
Overlaps
problem
Favourite

Overlaps

Age
11 to 14
Challenge level
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Can you find ways to put numbers in the overlaps so the rings have equal totals?
Gabriel's Problem
problem
Favourite

Gabriel's Problem

Age
11 to 14
Challenge level
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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
More Less is More
problem
Favourite

More Less is More

Age
7 to 14
Challenge level
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In each of these games, you will need a little bit of luck, and your knowledge of place value to develop a winning strategy.
Dozens
problem
Favourite

Dozens

Age
7 to 14
Challenge level
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Can you select the missing digit(s) to find the largest multiple?
What numbers can we make?
problem
Favourite

What numbers can we make?

Age
11 to 14
Challenge level
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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Square It
problem
Favourite

Square It

Age
11 to 16
Challenge level
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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.

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?

Cinema Problem
problem
Favourite

Cinema Problem

Age
11 to 14
Challenge level
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A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

Got It
problem
Favourite

Got It

Age
7 to 14
Challenge level
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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
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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?

Product Sudoku
problem
Favourite

Product Sudoku

Age
11 to 16
Challenge level
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The clues for this Sudoku are the product of the numbers in adjacent squares.

The Remainders Game
game
Favourite

The Remainders Game

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

Last Biscuit
game

Last Biscuit

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

Pair Products
problem
Favourite

Pair Products

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

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

Special Numbers
problem
Favourite

Special Numbers

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

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?