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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?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Charlie and Lynne 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?
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
A Sudoku with clues as ratios.
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...
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku with clues as ratios or fractions.
Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
Use the differences to find the solution to this Sudoku.
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
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?
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
How many different symmetrical shapes can you make by shading triangles or squares?
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four surrounding cells.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
A pair of Sudoku puzzles that together lead to a complete solution.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
You need to find the values of the stars before you can apply normal Sudoku rules.
A challenging activity focusing on finding all possible ways of stacking rods.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
This Sudoku combines all four arithmetic operations.
This Sudoku, based on differences. Using the one clue number can you find the solution?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.
Two sudokus in one. Challenge yourself to make the necessary connections.
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?
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. . . .