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There are 108 NRICH Mathematical resources connected to Working systematically, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Working systematicallyCan you use the clues to complete these 5 by 5 Mathematical Sudokus?
In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?
Can you do a little mathematical detective work to figure out which number has been wiped out?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you find the hidden factors which multiply together to produce each quadratic expression?
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.
Use the differences to find the solution to this Sudoku.
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?
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.
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 intersections between two diagonally adjacent squares.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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?
The clues for this Sudoku are the product of the numbers in adjacent squares.
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
There are lots of different methods to find out what the shapes are worth - how many can you find?
All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
Can you create a Latin Square from multiples of a six digit number?
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?
Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?
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?
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.
This is about a fiendishly difficult jigsaw and how to solve it using a computer program.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Five equations and five unknowns. Is there an easy way to find the unknown values?
To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?
Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
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.
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?
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
What is the smallest perfect square that ends with the four digits 9009?