3. How many?
The jelly design
wouldneed 200
ice cubes4.

Enough blocks?
There are exactly
enough..



Volume 12 (Solutions for: CIRCA 34, CIRCA 35 and CIRCA 36)

CIRCA 34: Solutions

Front cover/Coin count:
There are 57 coins in the chest. The puzzle can be solved by trial and improvement or using a table.
(In a table, patterns of repeating numbers are more obvious. A table of only multiples of 3 gets a solution
more quickly but the pattern is less obvious.)

Children could use their table to make up similar puzzles, e.g. “There were less than 100 soldiers. If
the soldiers lined up in threes or fours or fives or sixes, there was always one left over.” How many
soldiers?

Pages 2 and 3/Shield count
Pattern search
Outside: 8, 12, 16, 20, 24, 28, 32, 36
Inside: 1, 4, 9, 16, 25, 36, 49, 64
Total: 9, 16, 25, 36, 49, 64, 81, 100

Shield count quiz
1. +4 T, 2. Square R, 3. 52 O, 4. 100 H

Re-arranged the letters spell out THOR, the Norse god of Thunder.

Up to 6 x 6 arrays, there are more shields on the outside. For 7 x 7 arrays and larger, there are
more inside.

Pages 4 and 5/
Who does what?
Rules and jobs
Eric: 1, 4, 7, 10, 13, 16, .... The rule is add 3
Eric is a fisherman.
Thora: 1, 2, 4, 8, 16, 32, ... The rule is double successive terms
Thora is a weaver.
Olaf: 1, 2.5, 4, 5.5, 6, 7.5, ... The rule is add 1.5
Olaf is a blacksmith.
Godrun: 1, -3, -7, -11, -15, -19, ... The rule is minus 4
Godrun is a market trader.


Page 6 and 7/Einn, tveir, ...
In a group of 8, Hal should be number 1 in the circle. He should be 3rd in the circle for a group of 33.
For a group of 40 he should stand in position 17.

By filling in the table ‘Hal’s place’, children should find a repeating pattern and a doubling pattern of
odd numbers which they can use to make predictions. The pattern is quite sophisticated, linking
odd numbers with binary numbers.

Page 8 and 9/Patterns to infinity
Pattern 1: You can make 8 arrangements with five 1 x 2 rectangles. The different numbers of
arrangements produce the Fibonacci series of numbers: (1), 1, 2, 3, 5, 8. 13, 21, ...

Pattern 2: The sixth stone will have 21 runes on it. The series of triangle numbers begins: 1, 3, 6, 10,
15, 21, 28, 36, 45, ....

Pattern 3: 21 is the lowest number that can be made with one (21), two (15 + 6) or three leaves
(10 + 10 + 1).

Pattern 4: 31/32 of the fifth flag will be yellow.
Pattern 5: 8 cubes.

Fiery stone quiz

1. R, 2. A, 3. V, 4. E, 5. N
It spells out RAVEN. Odin, the chief Norse god, had two ravens, Huginn (thought) and Muginn (memory).
These two birds kept him informed of what was going on in the world.

Pages 10 and 11/Whose runes are whose?
Thora: C (means ‘be gentle’)
Astrid’s baby: D (means ‘wisdom’)
Grim: B (means ‘victory’)

There are 6 permutations possible, if one is wrong, at least one other will be as well.
4 runes gives 4! (24 permutations)
5 runes gives 5! (120 permutations)
6 runes gives 6! (720 permutations)

Pages 12 and 13/The saga of Eric the Red
1. Red 2. Blue (odd + even = odd, odd numbers are painted blue) 3. Green (red and blue mixed makes
purple; red and yellow mixed makes orange; yellow and blue mixed makes green) 4. Purple (Red: 100 +
100 + 50 = 250, Blue: 100 + 15 + 10 = 125 and Purple: 100 + 5 + 5 = 110) 5. Yellow
6. Orange (17 x 5 m and 5 x 3 m) 7. Red (24 has 6 factors, 50 and 28 only have 4 factors each)
8. The nearest set are the correct stepping stones. The colour of each stone reflects the correct
solutions of the previous seven puzzles.

Pages 14 and 15 /Are you puzzled?
What’s missing?
1. S, S (days of the week) 2. R and Y (colours of the rainbow)
3. E and S (planets in order from the Sun) Note: Pluto has been demoted. 4. S and E (One, Two,
Three, ...) 5. F and S (ordinal numbers: first, second, third, ...) 6. M and J (months of the year).

On the ship
Fenja: 9 apples. Egil: 3 Ingun: None. Pigs can’t talk. Gotthorn: 3 trips (you can’t make half a trip).
Thorolf: Because he was drawing a graph.

Shield pyramid addition














Cross number















Twin ships
The twin shops are 3 and 11.

Carrot value
A carrot is worth three onions.

onion = 1
apple = 2
carrot = 3
pear = 4
cabbage = 10.

Page 16 (back cover)/Square thinking
This seems quite a simple problem on the face of it. “64 squares, 65 if you count the one on the
outside.”) It isn’t quite so easy. As Alice shows, there are overlapping squares of 2 x 2, 3 x 3,
and so on.

The answers is 204 (64 + 49 + 36 + 25 + 16 + 9 + 4 + 1)

To get to the correct solution, children will have to be systematic. One way is to draw out a series of
small chessboard grids and work through each methodically. Alternatively, children can use the shortcut
of working out how many, say, 2 x 2 squares there are in a row, and then multiplying it by the number
in a column, which in this case is 7 x 7.

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CIRCA 35: Solutions

Front cover/Penguin puzzle:
Pippa is the Emperor penguin second from the right in the sixth row.

Pages 2 and 3/Positive and negative numbers
Quiz show
Shanta wins the trip. Here’s why...

Before the final question the scores stand at 1 for Shanta and 0 for Brad. Polar bears are only native
to the North Pole (Arctic) and so Brad’s answer is wrong and he gets a minus point. The final scores
are: Shanta 3 and Brad -1.

Back puzzle
Mike is 10 metres from his start position.

Minus money
(1) C, (2) A, (3) D and (4) B

Have you got the right altitude?
4 / 9 / 0
8 / -19 / E
7 / -9 / T
6 / -17 / I
2 / 19 / P
5 / -6 / S
1 / 17 / 0
3 / 6 / P

The secret word is OPPOSITE.

Pages 4 and 5/
Puzzling penguins
Rockhopper: +7, -8, +8, -3, -7 = -3
Chinstrap: +10, -8, +8, -3, -7 = 0
Emperor: +3, -10, -8, +12, +2 = -1
Macaroni: -10, +5, +5, -1, -3 = -2
Adelie: +5, +1, -7, -3, -1 = -5
King: -10, +5, +3, +8, -10, = -4


Page 6 and 7/Search for the snow creature
(1) B (-3°C), (2) I (-2°C), (3) G (-7°C), (4) F (-17°C),
(5) O (-15°C), (6) O (34°C), (7) T

Note: the drop in temperature on Day 5 is calculated from the real temperature of Day 4
and not the apparent wind chilled perceived temperature.

The secret word is BIGFOOT.
Bigfoot is the supposed North American cousin of the Yeti.

Page 8 and 9/Who lives on the fourth floor?
PGoldie Coin lives on the fourth floor. By deduction you will have discovered where the others lived...

Floor 15: Robin Banks
Floor 14: Baz Brass
Floor 13: Penny Galore
Floor 12: Roger Ruby
Floor 11: Amy Diamond
Floor 10: Bill Notes
Floor 9: Lady Dosh
Floor 8: Mandy Money
Floor 7: Major Cash
Floor 6: Arthur Dough
Floor 5: Debby Card
Floor 4: Goldie Coin
Floor 3: Sarah Copper
Floor 2: Lotsa Bread
Floor 1: Sylvia Spoon

Pages 10 and 11/Plus or minus
You will find all the answers on the spread.

Pages 12 and 13/Curves from straight lines

Asteroid



















Mystery curve

















Pages 14 and 15 /Are you puzzled?
Number tic-tac-toe
Have a go...









Iceberg wall











Iceberg rings














Iceberg square
















Bargain boots
Bridget paid the least.
£40.00 – £16.00 (discount) = £24.00
Bob paid the most.
£50.00 – £25.00 (discount) = £25.00


Icy golf
If you work backwards through the problem you will discover that:
Naomi took 8 shots
Bailey took 4 shots
Patesh took 2 shots
Justin took 9 shots

Forecast the broadcast
The last forecast before 7.00 am will be at 6.53 am.

The intervals between forecasts are 15 minutes. Throughout the day forecasts will be broadcast
at 08 minutes, 23 minutes, 38 minutes and 53 minutes past the hour.

Page 16 (back cover)/Temperature Tangle
The temperature at 8.00 am on Wednesday was -2°C.
From the story yo
u should have worked out all the
temperatures except for Friday noon (this isn’t given).









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CIRCA 36: Solutions

Front cover/Palettes puzzle:
The identical palette and brushes is the furthest on the right in the second row..

Pages 2 and 3/Design decisions
Sophie’s tiles
(A) translation (B) rotation (C) reflection

Sophie’s transformation quiz
1.
(e), 2. (h), 3. (s), 4. (a) and 5. (p)
The word spelt out by correct answers is ‘shape’.


Pages 4 and 5/
Frame maze
Page 6 and 7/Ice cubes
2. Missing lines
Completed drawings for D to F:



















Pages 8 and 9/Can you believe your eyes?
Diving board Some people find that the big penguin’s diving board view is difficult to hold on to!
(The steps’ risers change from facing right to facing left.)

Penguin perspective The penguins are all the same size. You knew that didn’t you! It’s the perspective
floor which fools the eye.

Hidden Faces The student’s professor is upside-down. The girl’s chin is the grandmother’s nose.

Pages 10 and 11/Knight's puzzle
The knight can make it in 11 moves. There are other, longer routes.

The numbers in the squares show the order of one of the ways they can all be reached using knight’s moves starting at 1. (This is hard to annotate as the knight has to go back many times to check all the squares he can reach from each position - can a more economical route be found?)





















Pages 12 and 13 /Remy paints a cycle
Remy investigates
3: one cycle 1,2 7: one cycle 3,4 1,6 5,2 9: two cycles 4,5 1,8 7,2 and 3,6
11: one cycle 5,6 1,10 9,2 7,4 3,8 15: See below
23: one cycle 12,11 1,22 21,2 19,4 15,8 7,16 9,14 5,18 13,10 3,20 17,6

Children will recognise that each pair of numbers created by the rules sums to the number being cycled.
For able children this can be demonstrated and justified algebraically.

When the starting number is a prime number the cycle contains all the possible combinations of pairs of
numbers that sum to the starting number (with the exception of 17 – are there others?).

Other odd numbers may need more that one cycle to exhibit all the possible pairs. For example, 15 has
3 cycles of pairs:










For even numbers the pairs form loops rather than cycles. Usually, the separate loops are linked and
have a final pair which includes zero.

Remy’s cycle begins an investigation in which a variety of questions can provide some fruitful starting
points. For example children can categorise* the types of number which create cycles, loops and spurs.

Pages 14 and 15 /Are you puzzled?
Brush count











Triangle brushes














Sold out!
Augusta sold two paintings at £70.00 and five at £20.00.

Check it
The third painting will have 24 white cells.
The tenth painting will have 220 white cells.
For any n x n grid, excluding the centre red cell, there are an equal number of red and white cells.
So the number of white cells for an n x n grid is 1/2(n2-1).

Who stole the Haywain?
Mr Brush stole the Haywain.

Page 16 (back cover)/How much?
In frame 4 the bottom set contains 1 more item than the set above. By subtracting the price of the top
set from the bottom set you get the price of the milk jug. The prices of the other items (even the price
of the individual mugs) can be found in a similar way.

The teapot is £7.00, the 4 mugs are £5.00 (£1.25p each), the sugar bowl is £3.00, the milk jug is £3.50
and the cake stand is £4.00.


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