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

### Advent Calendar 2011 - Secondary

##### Stage: 3, 4 and 5 Challenge Level:

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

### Magic Vs

##### Stage: 2 Challenge Level:

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

### 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?

### Find the Difference

##### Stage: 1 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

### Weights

##### Stage: 3 Challenge Level:

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

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

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

### First Connect Three

##### Stage: 2, 3 and 4 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

### Difference Sudoku

##### Stage: 3 and 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

### Shape Times Shape

##### Stage: 2 Challenge Level:

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

### Getting the Balance

##### Stage: 1 Challenge Level:

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

### Route Product

##### Stage: 2 Challenge Level:

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

### 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.

### Growing Garlic

##### Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

### 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. . . .

### 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?

### Coordinate Challenge

##### Stage: 2 Challenge Level:

Use the clues about the symmetrical properties of these letters to place them on the grid.

### Intersection Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

### Diagonal Sums Sudoku

##### Stage: 2, 3 and 4 Challenge Level:

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

### Torn Shapes

##### Stage: 2 Challenge Level:

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

### Product Sudoku 2

##### Stage: 3 and 4 Challenge Level:

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

### 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?

##### Stage: 2 Challenge Level:

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.

### Product Sudoku

##### Stage: 3, 4 and 5 Challenge Level:

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

### More Transformations on a Pegboard

##### Stage: 2 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

### Warmsnug Double Glazing

##### Stage: 3 Challenge Level:

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

### 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?

### Ratio Sudoku 1

##### Stage: 3 and 4 Challenge Level:

A Sudoku with clues as ratios.

### Are You Well Balanced?

##### Stage: 1 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

### 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?

### 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?

### 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.

### Lots of Lollies

##### Stage: 1 Challenge Level:

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

### Peaches Today, Peaches Tomorrow....

##### Stage: 3 and 4 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?

### What Shape and Colour?

##### Stage: 1 Challenge Level:

Can you fill in the empty boxes in the grid with the right shape and colour?

### 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?

### A Square of Numbers

##### Stage: 2 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

### Trebling

##### Stage: 2 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

### 5 on the Clock

##### Stage: 2 Challenge Level:

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

### Symmetry Challenge

##### Stage: 2 Challenge Level:

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

##### Stage: 3 Challenge Level:

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

### Cinema Problem

##### Stage: 3 and 4 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.

### Counting Cards

##### Stage: 2 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

##### Stage: 1 Challenge Level:

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

### Sealed Solution

##### Stage: 2 Challenge Level:

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

### 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.

### Two Primes Make One Square

##### Stage: 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

### The Third Dimension

##### Stage: 1 and 2 Challenge Level:

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?