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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?"
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
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 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.
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...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Given the products of adjacent cells, can you complete this Sudoku?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
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?
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?
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 Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
A pair of Sudoku puzzles that together lead to a complete solution.
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
Two sudokus in one. Challenge yourself to make the necessary connections.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
This sudoku requires you to have "double vision" - two Sudoku's for the price of one
You need to find the values of the stars before you can apply normal Sudoku rules.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
This Sudoku combines all four arithmetic operations.
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
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?
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. . . .