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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. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?"
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Given the products of adjacent cells, can you complete this Sudoku?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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.
An environment which simulates working with Cuisenaire rods.
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.
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?
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...
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?
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?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Follow the clues to find the mystery number.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of diagonally opposite cells - can you complete this Sudoku?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
Can you make square numbers by adding two prime numbers together?
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
The clues for this Sudoku are the product of the numbers in adjacent squares.
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
An investigation that gives you the opportunity to make and justify predictions.
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
A game that tests your understanding of remainders.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
A game in which players take it in turns to choose a number. Can you block your opponent?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
Can you complete this jigsaw of the multiplication square?