Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A few extra challenges set by some young NRICH members.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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 letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
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?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
Can you find all the different ways of lining up these Cuisenaire rods?
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....?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
The pages of my calendar have got mixed up. Can you sort them out?
In this matching game, you have to decide how long different events take.
You need to find the values of the stars before you can apply normal Sudoku rules.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
If you had 36 cubes, what different cuboids could you make?
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.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?