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There are 184 NRICH Mathematical resources connected to Working systematically, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Working systematicallyDo you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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?
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?
Can you work out what step size to take to ensure you visit all the dots on the circle?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
There are lots of ideas to explore in these sequences of ordered fractions.
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
How many different symmetrical shapes can you make by shading triangles or squares?
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.
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 game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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?
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...
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 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?
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?
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?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Is there an efficient way to work out how many factors a large number has?
Can you create a Latin Square from multiples of a six digit number?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.