Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A few extra challenges set by some young NRICH members.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

You need to find the values of the stars before you can apply normal Sudoku rules.

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

How many different symmetrical shapes can you make by shading triangles or squares?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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.

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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?

Four small numbers give the clue to the contents of the four surrounding cells.

Find out about Magic Squares in this article written for students. Why are they magic?!

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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.

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

A pair of Sudoku puzzles that together lead to a complete solution.

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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.

A challenging activity focusing on finding all possible ways of stacking rods.