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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?
Given the products of adjacent cells, can you complete this Sudoku?
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?"
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.
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...
A game in which players take it in turns to choose a number. Can you block your opponent?
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths. . . .
A game that tests your understanding of remainders.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .
What is the smallest number with exactly 14 divisors?
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
Can you find a way to identify times tables after they have been shifted up?
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.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
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?
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.
Can you find what the last two digits of the number $4^{1999}$ are?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What is the smallest number of answers you need to reveal in order to work out the missing headers?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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.
How many zeros are there at the end of the number which is the product of first hundred positive integers?
Find the highest power of 11 that will divide into 1000! exactly.
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 clues for this Sudoku are the product of the numbers in adjacent squares.
Can you find any perfect numbers? Read this article to find out more...
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?