A challenging activity focusing on finding all possible ways of stacking rods.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
Use the clues about the symmetrical properties of these letters to place them on the grid.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A few extra challenges set by some young NRICH members.
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Try out the lottery that is played in a far-away land. What is the chance of winning?
In how many ways can you stack these rods, following the rules?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
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?
Can you find all the different triangles on these peg boards, and find their angles?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train can continue its journey?
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....?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Can you use the information to find out which cards I have used?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
In this matching game, you have to decide how long different events take.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
Using the statements, can you work out how many of each type of rabbit there are in these pens?