Secondary summer challenges 2023

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Can you describe this route to infinity? Where will the arrows take you next?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

These Olympic quantities have been jumbled up! Can you put them back together again?

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?

In each of these games, you will need a little bit of luck and your knowledge of place value to develop a winning strategy.

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.

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?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

What happens when you add a three digit number to its reverse?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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?

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?

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

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.

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

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

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

By selecting digits for an addition grid, what targets can you make?

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...

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Can you find ways to put numbers in the overlaps so the rings have equal totals?

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?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Can you crack these cryptarithms?

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.

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?