A few extra challenges set by some young NRICH members.
Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.
You need to find the values of the stars before you can apply normal Sudoku rules.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
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?
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
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.
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
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?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Given the products of adjacent cells, can you complete this Sudoku?
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?
In this matching game, you have to decide how long different events take.
This challenge extends the Plants investigation so now four or more children are involved.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?
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.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
A challenging activity focusing on finding all possible ways of stacking rods.
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?
Can you use the information to find out which cards I have used?
Four friends must cross a bridge. How can they all cross it in just 17 minutes?
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.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
How many possible necklaces can you find? And how do you know you've found them all?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
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.