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?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Pentagram Pylons - can you elegantly recreate them? Or, the
European flag in LOGO - what poses the greater problem?
Just four procedures were used to produce a design. How was it
done? Can you be systematic and elegant so that someone can follow
Can you recreate these designs? What are the basic units? What
movement is required between each unit? Some elegant use of
procedures will help - variables not essential.
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
This Sudoku combines all four arithmetic operations.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
Move your counters through this snake of cards and see how far you
can go. Are you surprised by where you end up?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
What is the best way to shunt these carriages so that each train
can continue its journey?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Two sudokus in one. Challenge yourself to make the necessary
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
A Sudoku with clues as ratios.
A Sudoku with a twist.
Four small numbers give the clue to the contents of the four
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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....?
This activity investigates how you might make squares and pentominoes from Polydron.
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. . . .
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.