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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...
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. . . .
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?"
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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 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 replace the letters with numbers? Is there only one solution in each case?
Given the products of adjacent cells, can you complete this Sudoku?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
An investigation that gives you the opportunity to make and justify predictions.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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 these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
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?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Follow the clues to find the mystery number.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Given the products of diagonally opposite cells - can you complete this Sudoku?
What could the half time scores have been in these Olympic hockey matches?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
In how many ways can you stack these rods, following the rules?
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.