There are **132** NRICH Mathematical resources connected to **Working systematically**, you may find related items under Thinking Mathematically.

Challenge Level

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?

Challenge Level

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Challenge Level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Challenge Level

Use the differences to find the solution to this Sudoku.

Challenge Level

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.

Challenge Level

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. . . .

Challenge Level

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Challenge Level

Given the products of diagonally opposite cells - can you complete this Sudoku?

Challenge Level

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?

Challenge Level

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?

Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

Challenge Level

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Challenge Level

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?

Challenge Level

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?

Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Challenge Level

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?

Challenge Level

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Challenge Level

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?

Challenge Level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Challenge Level

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly Â£100 if the prices are Â£10 for adults, 50p for pensioners and 10p for children.

Challenge Level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Challenge Level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Challenge Level

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...

Challenge Level

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?

Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Challenge Level

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?

Challenge Level

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?

Challenge Level

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Read this article to find out more about the inspiration for NRICH's game, Phiddlywinks.

Challenge Level

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Challenge Level

In this game you are challenged to gain more columns of lily pads than your opponent.

Challenge Level

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Challenge Level

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Challenge Level

By selecting digits for an addition grid, what targets can you make?

Challenge Level

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

Challenge Level

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. . . .

Challenge Level

A challenging activity focusing on finding all possible ways of stacking rods.

Challenge Level

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

Challenge Level

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Challenge Level

This challenge extends the Plants investigation so now four or more children are involved.

In this article, the NRICH team describe the process of selecting solutions for publication on the site.