There are 344 NRICH Mathematical resources connected to Working systematically, you may find related items under Thinking Mathematically.Broad Topics > Thinking Mathematically > Working systematically
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Have a go at balancing this equation. Can you find different ways of doing it?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these numbers to the nearest whole number?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
How many possible necklaces can you find? And how do you know you've found them all?
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you use the information to find out which cards I have used?
What could the half time scores have been in these Olympic hockey matches?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?
These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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. . . .
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?
Use the clues about the symmetrical properties of these letters to place them on the grid.
A Sudoku with clues given as sums of entries.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
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?
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.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
A Sudoku with clues as ratios.