Extension puzzles and tasks

1
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.

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A1
A2
Carpet Sales
Mr and Mrs Brown
A shop increased the price of its carpets by
20 Sales of the carpets dropped by 20 Did the
shops 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?
A3
A4
Eights and Nines
At The Table
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?
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?
3
A5
A6
Cash Point
Mashed Potatoes
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 Joys 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 out the 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?
A7
A8
Battleships
____ _
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.
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?
4
A9
A10
Overlap
Bracelets
5/6 of the circle is shaded pink 4/5 of the
hexagon is shaded yellow
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?
Area of 15 circles Area of ? hexagons
A11
A12
Extreme Sudoku
Word Sums
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.
Each letter in the following puzzles represents a
number between 0 and 9. No two letters can
represent the same number.
This one has 16 solutions can you find them all?
5
B1
B2
Builder's Dilemma
Routes to Victory
A builder can build either luxury houses or
standard houses on a plot of land. Planning
regulations prevent the builder from building
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.
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 Blackburns score first the
sequence could be 0-0 ? 0-1 ? 1-1? 2-1 or 0-0
? 1-0? 1-1? 2-1 or 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?
B3
B4
Cutting Problem
Example
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.
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.
6
B5
B6
Two Candles Burn
Broom Handles
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?
B7
B8
What Time Is It?
Magic Band
Exactly how many minutes is it before six oclock
if 50 minutes ago it was four times as many
minutes past three oclock?
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.
7
B9
B10
Folded Sheet
Painted Cube
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.
A 6 x 6 cube is painted red. It is then cut up
into a number of identical cubes as shown in the
picture.

• How many of the cubes have
• 3 red faces
• 2 red faces
• 1 red face
• 0 red faces

What would the answers be for an n x n cube? Can
you find a pattern that works for cuboids?
B11
B12
Watches
Ratio
Grannys watch gains 30 minutes every hour,
whilst Grandpas watch loses 30 minutes every
hour. At midnight, they both set their watches
to the correct time of 12 oclock. What is
the correct time when their two watches next
agree?
The ratio ab is 12, the ratio ac is 23, the
ratio ce is 14 and the ratio de is 25 What
is the ratio bd in its lowest terms?
8
C1
C2
Figure It Out
Rectangle Problem
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 (v5 v20)
cm long and v8 cm wide. A small rectangle v2 cm
long and v5 cm wide is cut out of the piece of
card. What percentage of the original rectangle
remains?
ROWS G Total is 31 H A plus B equals F there are
no 3s J Two 7s surround two boxes totalling 4 K A
is lower than F L Contains two 5s and two 2s M
Contains two 3s and two 6s
COLUMNS A Two 2s and two 5s four numbers are
odd B Two 3s and two 7s all numbers are odd C
Total is 31 L is twice G D Only one even
number E Total is 30 F Two 4s, two 6s and two 8s
C3
C4
Picture Puzzle
Peg
Which is a better fit a square peg in a round
hole or a round peg in a square hole?
The diagram shows a semi-circle and an isosceles
triangle which have equal areas. What is the
value of tan x
9
C5
C6
ABC
Word Multiplication
In this multiplication each letter represents a
different digit between 0 and 9.
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.
C7
C8
Pathological
Word Division
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 long-division problem, each letter
represents a different digit between 0 and 9.
EXAMPLE
10
C9
C10
Split Square
WindowPain
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?
C11
C12
Circles
What's my age again?
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?
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.