Challenge Level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

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The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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Using the statements, can you work out how many of each type of rabbit there are in these pens?

Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

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Two sudokus in one. Challenge yourself to make the necessary connections.

Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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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?

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Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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?

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This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Challenge Level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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Two sudokus in one. Challenge yourself to make the necessary connections.

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What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Can you make square numbers by adding two prime numbers together?

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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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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?

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How many possible necklaces can you find? And how do you know you've found them all?

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A few extra challenges set by some young NRICH members.

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This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?