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Resources tagged with Working systematically similar to The Remainders Game:

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

Product Sudoku

Stage: 3 Challenge Level:

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

A First Product Sudoku

Stage: 3 Challenge Level:

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

Multiples Sudoku

Stage: 3 Challenge Level:

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

How Old Are the Children?

Stage: 3 Challenge Level:

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Ones Only

Stage: 3 Challenge Level:

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Stage: 3 Challenge Level:

A few extra challenges set by some young NRICH members.

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?

Crossing the Town Square

Stage: 2 and 3 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Reach 100

Stage: 2 and 3 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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.

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?

Football Sum

Stage: 3 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Colour Islands Sudoku

Stage: 3 Challenge Level:

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

Stage: 3 Challenge Level:

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Stage: 3 Challenge Level:

You need to find the values of the stars before you can apply normal Sudoku rules.

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...

Peaches Today, Peaches Tomorrow....

Stage: 3 Challenge Level:

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Two and Two

Stage: 3 Challenge Level:

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

Twinkle Twinkle

Stage: 2 and 3 Challenge Level:

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Multiples Grid

Stage: 2 Challenge Level:

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?

Neighbours

Stage: 2 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Cinema Problem

Stage: 3 Challenge Level:

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.

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?

Pair Sums

Stage: 3 Challenge Level:

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five 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?

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?

Curious Number

Stage: 2 Challenge Level:

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?

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?

Cayley

Stage: 3 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Magic Potting Sheds

Stage: 3 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?

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?

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

More on Mazes

Stage: 2 and 3

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Medal Muddle

Stage: 3 Challenge Level:

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

The Moons of Vuvv

Stage: 2 Challenge Level:

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Stage: 3 Challenge Level:

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

Weights

Stage: 3 Challenge Level:

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

Mystery Matrix

Stage: 2 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Sweets in a Box

Stage: 2 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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?

Counting on Letters

Stage: 3 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Stage: 3 Challenge Level:

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Multiplication Squares

Stage: 2 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

How Long Does it Take?

Stage: 2 Challenge Level:

In this matching game, you have to decide how long different events take.

It Figures

Stage: 2 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Inky Cube

Stage: 2 and 3 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?

A Bit of a Dicey Problem

Stage: 2 Challenge Level:

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Family Tree

Stage: 2 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

A-magical Number Maze

Stage: 2 Challenge Level:

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!