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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

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.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

There were 22 legs creeping across the web. How many flies? How many spiders?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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 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 work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

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

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Use these head, body and leg pieces to make Robot Monsters which are different heights.