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...

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?

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

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?"

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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

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.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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. . . .

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Use the differences to find the solution to this Sudoku.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

How many different symmetrical shapes can you make by shading triangles or squares?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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.

Use the clues about the shaded areas to help solve this sudoku

Four small numbers give the clue to the contents of the four surrounding cells.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

A pair of Sudoku puzzles that together lead to a complete solution.