Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Factorial one hundred (written 100!) has 24 noughts when written in full and that 1000! has 249 noughts? Convince yourself that the above is true. Perhaps your methodology will help you find the. . . .
A game that tests your understanding of remainders.
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.
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?"
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 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?
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.
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. . . .
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...
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you work out what size grid you need to read our secret message?
A game in which players take it in turns to choose a number. Can you block your opponent?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Given the products of adjacent cells, can you complete this Sudoku?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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?
Can you find any perfect numbers? Read this article to find out more...
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
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?
Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.
Make a line of green and a line of yellow rods so that the lines differ in length by one (a white rod)
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
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.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Substitution and Transposition all in one! How fiendish can these codes get?
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. . . .
Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.
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?
Find the highest power of 11 that will divide into 1000! exactly.
Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
What is the smallest number with exactly 14 divisors?
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.
The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .
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. . . .