Extension puzzles and tasks

• The next few slides contain a variety of tasks and puzzles that should challenge and stretch you.

• Some may need to be printed off before you can attempt them.

• If you submit an answer, please write the title of the puzzle at the top of your paper so we can check it for you. Choose whichever one you would like to do. Vivos rewarded for a good attempt.

A shop increased the price of its carpets by 20%

Sales of the carpets dropped by 20%

Did the shop’s profits from carpet sales rise or fall?

When Mr and Mrs Brown married, the sum of their ages was 44.

The difference between their ages was one-sixth for the sum of their ages 10 years before their marriage.

How old were Mr and Mrs Brown when they married?

The integers from 1 to 9 are listed on a whiteboard

1, 2, 3, 4, 5, 6, 7, 8, 9

The mean of all the numbers in the list is 5.

Some extra eights and nines are added to the list. The mean of the list is now 7.3

How many eights and nines are added?

There are six people in the Green family: 2 parents, 2 girls and 2 boys.They all sit around the table as shown below.

The two girls never sit opposite or next to each other.The two boys never sit opposite or next to each other.The two parents never sit opposite or next to each other.How do the Green family sit at the table?

A1 A2

A3 A4

Jay and Joy are peeling potatoes for a dinner party.

They each start with the same number of potatoes to peel.

Every minute, each of them peels two potatoes, and Jay sneakily throws one of his unpeeled potatoes on Joy’s pile.

After 10 minutes, Joy has three times as many potatoes still to peel as Jay.

How many potatoes did each of them have to start with?

Flash Jack went to the cash point. He drew out the same amount of money as he had in his pocket. He then spent £40 on new clothes.

Jack went back to the cash point. He drew outthe same amount of money as he had in his pocket. He then spent a further £40 on new clothes.

Jack did this a third time.He then had no money left.How much money did he have with him to start?

The diagram shows a rectangular box.

The areas of the faces are 3, 12 and 25 square centimetres. What is the volume of the box?

If the areas of the faces are p, q and r, what is the volume of the box in terms of p, q and r?

Aircraft Carrier:

Battleship:

Cruiser:

Destroyer:

Try to find the vessels in the diagram. Some parts of boats or sea squares have already been filled in. A number next to a row or column refers to the number of occupied squares in that row or column. Boats may be positioned horizontally or vertically, but not diagonally. No two boats or parts of boats are in adjacent squares – horizontally, vertically or diagonally.

0 3 0 4 3 2 4 1 0 30322315040

A5 A6

A7 A8

3cm2

25cm2

12cm2

A9 A10

A11 A12

5/6 of the circle is shaded pink

4/5 of the hexagon is shaded yellow

Area of 15 circles = Area of ? hexagons

There are 800 women in a village. 3% of the women wear 5 bracelets. Of the remaining

97%, ½ wear 3 bracelets and ½ wear 7 bracelets. How many

bracelets are worn altogether?

Each letter in the following puzzles represents a number between 0 and 9. No two letters can represent the same

number.S A V E

+ M O R EM O N E Y

O N E+ O N E

T W O

This one has 16 solutions – can you find them

all?

Place the digits 1 to 7 into the empty squares

so that each digit appears once in every row and column, once in each of the outlined

white regions, and once in each of the seven

grey squares.

4 52

71 5

1 3 42

3

15

These parts of

the shape should lie flat on the desk

These parts of

the shape should

stick up at right

angles to the desk

Can you make the shape from a

piece of card. You can only cut and fold the card

– you are not allowed to use

glue or sellotape.

The object of this puzzle to create a "fence" that connects dots horizontally or vertically, but not diagonally. The numbers in the grid indicate how many sides of the fence go around that space. Try to find as many different solutions as you can for each problem. In the example shown, there are three different solutions.

Example

B1 B2

B3 B4

In a recent football match, Blackburn Rovers beat Newcastle United 2-1. What could the half-time score have been?

How many different ‘routes’ are there to any final score? For example, for the above match, putting Blackburn’s score first the sequence could be:

0-0 → 0-1 → 1-1→ 2-1or 0-0 → 1-0→ 1-1→ 2-1or 0-0 → 1-0→ 2-0→ 2-1

So in this case there are three routes.

Is there a pattern between the final score and the number of routes?

A builder can build either luxury houses or standard houses on a plot of land.

Planning regulations prevent the builder frombuilding more than 30 houses altogether, and he wants to build at least 5 luxury houses and at least 10 standard houses.

Each luxury house requires 300m2 of land, and each standard house require 150m2 of land. The total area of the plot is 6500m2.

Given that the profit on a luxury house is £14000 and the profit on a standard house is £9000, find how many time of each house he should build to maximise his profit.

One night two candles one of which was 3cm longer than the other were lit.

The longer one was lit at 5.30pm and the shorter one at 7pm.

At 9.30pm they were both the same length.

The longer one burned out at 11.30pm and the shorter one burned out at 11pm.

How long was each candle originally?

A shop sells handles for garden brooms which are made up of cylinders of

wood, diameter 5cm.

I bought three of these and, to keep them

together, put a rubber band round each end of

the bundle. How long will each rubber band be?

Exactly how many minutes is it before six o’clock if 50 minutes ago it was four times as many minutes past three

o’clock?

?

Can you make this shape

from a piece of card. You can only cut and fold the

card – you are not allowed

to use glue or sellotape.

B5 B6

B7 B8

B9 B10

B11 B12

1 8 7 4

2 3 6 5

Divide a rectangular piece of paper into eight squares and number them on one side only as shown in the diagram.

Now try and fold the sheet so that the squares are in order with 1 face up on top through to 8 at the bottom.

1 8 2 7

4 5 3 6

Granny’s watch gains 30 minutes every hour, whilst Grandpa’s watch loses 30 minutes every hour. At midnight, they both set their watches to the correct time of 12 o’clock. What is the correct time when their two watches next agree?

A 6 x 6 cube is painted red. It is then cut up into a number of identical cubes as shown in the picture.

What would the answers be for an n x n cube?

Can you find a pattern that works for cuboids?

How many of the cubes havei) 3 red facesii) 2 red facesiii) 1 red faceiv) 0 red faces

The ratio a:b is 1:2, the ratio a:c is 2:3, the ratio c:e is 1:4 and the ratio d:e is 2:5

What is the ratio b:d in its lowest terms?

The numbers 1 to 9 each appear four times in the grid, with no two identical or consecutive numbers horizontally or vertically adjacent. Where a number appears more than once in a row or column, it is specifically stated in the clues.

A large rectangular piece of card is (√5 + √20) cm long and √8 cm wide.

A small rectangle √2 cm long and √5 cm wide is cut out of the piece of card.

What percentage of the original rectangle remains?

C1 C2

C3 C4

(√5 + √20)

√8√5

√2

ROWSG Total is 31H A plus B equals F; there are no 3sJ Two 7s surround two boxes totalling 4K A is lower than FL Contains two 5s and two 2sM Contains two 3s and two 6sCOLUMNSA Two 2s and two 5s; four numbers are oddB Two 3s and two 7s; all numbers are oddC Total is 31; L is twice GD Only one even numberE Total is 30F Two 4s, two 6s and two 8s

A B C D E FGHJKLM

x°The diagram shows a semi-circle and

an isosceles triangle which

have equal areas. What is the value

of tan x°

Which is a better fit – a square peg in a round hole or a round peg in a square hole?

C5 C6

C7 C8

C1↓ A2↓

B2 → A1

← B1←

C1 →

C2←

A2↑ B1↑ A2↑

Each row and column is to have each of the letters A, B

and C, and two empty squares. The letter outside the grid shows the first or

second letter in the direction of the arrow.

In this long-division problem, each letter

represents a different digit between 0 and 9.

4 3 1 4 6 5 1 7 7 12218534347

START

FINISH

2 4 3 44333

START

FINISH

EXAMPLE

Form a pathway from the box marked ‘start’ to the box marked ‘FINISH’ moving horizontally, vertically (but not diagonally). The number at the beginning of every row and column indicates how many boxes in that row or column your pathway must pass through.

In this multiplication each letter represents a different digit between 0

and 9.

F G H J KX 4K J H G F

B F CA B C D E D C D

A B CB G C CB F G H

G C DG C D

C9 C10

C11 C12

A large window consists of six square panes of glass as shown.

Each pane is x m by x m and all the dividing wood is y m wide.

The total area of the glass is 1.5m2 and the total area of the dividing wood is 1m2. Find the values of x and y.

The diagram shows a square with two lines from a corner to the middle of an opposite side. The rectangle fits exactly inside these two lines and the square itself.

What fraction of the square is occupied by the shaded rectangle?

When asked how old she was the teacher replied:

My age in years is not prime but odd and when reversed and added to my age you have a perfect square.

Or you can reverse and subtract, and again you have a perfect square.

The diagram shows two circles and four equal semi-circular arcs.

The area of the inner shaded circle is 1.

What is the area of the outer circle?