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.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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.

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

Delight your friends with this cunning trick! Can you explain how it works?

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

There are nasty versions of this dice game but we'll start with the nice ones...

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

This article suggests some ways of making sense of calculations involving positive and negative numbers.

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Got It game for an adult and child. How can you play so that you know you will always win?

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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.

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Here is a chance to play a version of the classic Countdown Game.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

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?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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?

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?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .

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

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

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!

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?