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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Here is a chance to play a version of the classic Countdown Game.
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?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
An odd version of tic tac toe
If you have only four weights, where could you place them in order to balance this equaliser?
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?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
An environment which simulates working with Cuisenaire rods.
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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!
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Can you find just the right bubbles to hold your number?
Can you complete this jigsaw of the multiplication square?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How many different rhythms can you make by putting two drums on the wheel?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Move just three of the circles so that the triangle faces in the opposite direction.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you find all the different triangles on these peg boards, and find their angles?
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Match the halves.