Given the products of diagonally opposite cells - can you complete this Sudoku?

The clues for this Sudoku are the product of the numbers in adjacent squares.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

A game that tests your understanding of remainders.

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Given the products of adjacent cells, can you complete this Sudoku?

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. . . .

Can you complete this jigsaw of the multiplication square?

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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!

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.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you work out what size grid you need to read our secret message?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Can you find a way to identify times tables after they have been shifted up?

If you have only four weights, where could you place them in order to balance this equaliser?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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.

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.

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 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?"

A game in which players take it in turns to choose a number. Can you block your opponent?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

Find the highest power of 11 that will divide into 1000! exactly.

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?

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?

An investigation that gives you the opportunity to make and justify predictions.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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.

Can you find any perfect numbers? Read this article to find out more...

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.

Can you find what the last two digits of the number $4^{1999}$ are?

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?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

Use the interactivities to complete these Venn diagrams.

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?