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Resources tagged with Working systematically similar to Think of Two Numbers:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

Special Numbers

Stage: 3 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?

Summing Consecutive Numbers

Stage: 3 Challenge Level:

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?

American Billions

Stage: 3 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...

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Ben's Game

Stage: 3 Challenge Level:

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Consecutive Negative Numbers

Stage: 3 Challenge Level:

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

Product Sudoku

Stage: 3, 4 and 5 Challenge Level:

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

9 Weights

Stage: 3 Challenge Level:

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?

M, M and M

Stage: 3 Challenge Level:

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

Squares in Rectangles

Stage: 3 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?

Two and Two

Stage: 2 and 3 Challenge Level:

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

Stage: 3 Challenge Level:

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

Consecutive Numbers

Stage: 2 and 3 Challenge Level:

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

Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Weights

Stage: 3 Challenge Level:

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

Sticky Numbers

Stage: 3 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Number Daisy

Stage: 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?

Where Can We Visit?

Stage: 3 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?

Difference Sudoku

Stage: 3 and 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

More Magic Potting Sheds

Stage: 3 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?

Alphabetti Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku requires you to do some working backwards before working forwards.

Triangles to Tetrahedra

Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

Stage: 3 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level:

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?

Wallpaper Sudoku

Stage: 3 and 4 Challenge Level:

A Sudoku that uses transformations as supporting clues.

Ratio Sudoku 1

Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

Integrated Product Sudoku

Stage: 3 and 4 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.

Twin Line-swapping Sudoku

Stage: 4 Challenge Level:

A pair of Sudoku puzzles that together lead to a complete solution.

Seasonal Twin Sudokus

Stage: 3 and 4 Challenge Level:

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

A First Product Sudoku

Stage: 3 Challenge Level:

Given the products of adjacent cells, can you complete this Sudoku?

Magic Caterpillars

Stage: 4 and 5 Challenge Level:

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Factor Lines

Stage: 2 and 3 Challenge Level:

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

Latin Squares

Stage: 3, 4 and 5

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.

Integrated Sums Sudoku

Stage: 3 and 4 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. . . .

Rainstorm Sudoku

Stage: 4 Challenge Level:

Use the clues about the shaded areas to help solve this sudoku

Rectangle Outline Sudoku

Stage: 3 and 4 Challenge Level:

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Twin Corresponding Sudoku III

Stage: 3 and 4 Challenge Level:

Two sudokus in one. Challenge yourself to make the necessary connections.

Product Doubles Sudoku

Stage: 3 and 4 Challenge Level:

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

Sociable Cards

Stage: 3 Challenge Level:

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

A Long Time at the Till

Stage: 4 and 5 Challenge Level:

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

First Connect Three for Two

Stage: 2 and 3 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Olympic Logic

Stage: 3 and 4 Challenge Level:

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

Stage: 3, 4 and 5 Challenge Level:

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

Colour Islands Sudoku 2

Stage: 3, 4 and 5 Challenge Level:

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

Bochap Sudoku

Stage: 3 and 4 Challenge Level:

This Sudoku combines all four arithmetic operations.

Product Sudoku 2

Stage: 3 and 4 Challenge Level:

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

An Introduction to Magic Squares

Stage: 3 and 4 Challenge Level:

Four small numbers give the clue to the contents of the four surrounding cells.

Fence It

Stage: 3 Challenge Level:

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

Isosceles Triangles

Stage: 3 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?