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?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A few extra challenges set by some young NRICH members.
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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.
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
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.
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?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
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?
Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E
Given the products of adjacent cells, can you complete this Sudoku?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
A challenging activity focusing on finding all possible ways of stacking rods.
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?