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.

Can you explain the strategy for winning this game with any target?

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?

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

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

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

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?

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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?

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

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?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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!

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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.

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?

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?

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

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

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.

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

This dice train has been made using specific rules. How many different trains can you make?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?