We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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?
A Sudoku with a twist.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Imagine a stack of numbered cards with one on top. Discard the top,
put the next card to the bottom and repeat continuously. Can you
predict the last card?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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?
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.
You need to find the values of the stars before you can apply normal Sudoku rules.
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.
Four numbers on an intersection that need to be placed in the
surrounding cells. That is all you need to know to solve this
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.
Solve the equations to identify the clue numbers in this Sudoku problem.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Label this plum tree graph to make it totally magic!
A Sudoku with clues as ratios or fractions.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This Sudoku, based on differences. Using the one clue number can you find the solution?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Bellringers have a special way to write down the patterns they
ring. Learn about these patterns and draw some of your own.
This sudoku requires you to have "double vision" - two Sudoku's for
the price of one
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?
A Sudoku with clues as ratios.
Two sudokus in one. Challenge yourself to make the necessary
Explore this how this program produces the sequences it does. What
are you controlling when you change the values of the variables?
A pair of Sudoku puzzles that together lead to a complete solution.
This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?
Four small numbers give the clue to the contents of the four
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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. . . .
This Sudoku combines all four arithmetic operations.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
An irregular tetrahedron is composed of four different triangles.
Can such a tetrahedron be constructed where the side lengths are 4,
5, 6, 7, 8 and 9 units of length?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
A Sudoku that uses transformations as supporting clues.
This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.
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?
A Sudoku with clues given as sums of entries.
A Sudoku based on clues that give the differences between adjacent cells.
Each of the main diagonals of this sudoku must contain the numbers
1 to 9 and each rectangle width the numbers 1 to 4.
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.