i
(Please note some solutions are dependent on images and are omitted here. If you need a
particular solution please e-mail).

Volume 6 (issues 16, 17 and 18)

CIRCA 16: Solutions

Front cover/Aliens are invading: The two identical flying saucers are third row down, fourth
on right and bottom row, third on right.

Pages 2 and 3/Alien money
With UK coins it is not possible to make 4p or 9p or any amount with 4 or 9 in them
(e.g. 42p, 96p) unless you use two coins of the same denomination.

Another 2p and another 20p are all that are needed to make all amounts under £1.

It is possible to buy all the chocolate bars without using two coins of the same value.

Shooting Star: 16 + 8 = 24
Martian Bar: 32 + 16 + 8 + 1 = 57
Solar System: 64 + 16 + 2 + 1 = 83
Galactic Slab: 64 + 32 + 4 + 1 = 101 = 1.01 Zut

All numbers under 100 (and up to 127) can be made using no more than one Zuton coin
of the same value.


Pages 4 and 5/What's money?
No solutions.


Page 6 and 7/Starchart magic
A solution is given on page 14 of the magazine (CIRCA 16).

Pages 8 and 9/Money pit
There are four different routes that lead to a successful exit. Requires visual solution.
Please e-mail.

Pages 10 and 11/Corn circles
No solutions

Pages 12 and 13/Eyes and teeth
The player going first should always win providing she always plays a ‘best’ game.

Pages 14 and 15/Are you puzzled?
Upside down
Requires visual solution. Please e-mail.

Hairy addition
6216 + 2121 = 8337.

Spacemaze
Requires visual solution. Please e-mail.

Bungalow tour
Mrs Adams is right about her bungalow (1) and it is also true about bungalow (3).
It is not possible with bungalow (2).

Fraction faces
Third + third + third = 1
Sixth + third + half = 1


Operations with 3
3 x 3 + 3 ÷ 3 - 3 = 1
3 + 3 - 3 + 3 ÷ 3 = 2
3 + 3 - 3 + 3 - 3 = 3
3 + 3 + 3 + 3 ÷ 3 = 4
3 x 3 + 3 + 3 ÷ 3 = 5
3 + 3 - 3 x 3 - 3 = 6
3 x 3 + 3 ÷ 3 + 3 = 7
3 x 3 x 3 - 3 ÷ 3 = 8
3 + 3 + 3 x 3 ÷ 3 = 9
3 x 3 x 3 + 3 ÷ 3 = 10

Page 16 (back cover)/Don't get wet!
Alice and the rest of the party, including the rucksack, can get to the other side without getting
wet in eleven crossings. See table.
AACCR
(1) AA R –> CC
(2) AA C R <– C
(3) AA –> CCR
(4) AA C <– C R
(5) A C –> A CR
(6) A C C <– A R
(7) A –> A CCR
(8) A C <– A CR
(9) C –> AACR
(10) C C <– AA R
(11) –> AACCR TOP.


CIRCA 17: Solutions

Front cover/Tiz-Tap
See page 14 of the magazine (CIRCA 17).

Pages 2 and 3/What does ...?
Please e-mail for solution.

Pages 4 and 5/Puzzling mirrors
Mirror puzzles
All the words have symmetry, BOB is symmetrical both
horizontally and vertically. CHOICE, BOOK, DECIDE, KID and COOK have horizontal symmetry.
TIMOTHY, MUM and AUTO are symmetrical about the vertical axis if they are laid as they are on
page 5. There are no other palindromic words with horizontal symmetry known to the editors.
Other words that have horizontal symmetry when written one letter below the last are:
HAM, WIT, OX, MOAT, WAX and so on. The easiest approach to finding words is for children to
first find which letters are symmetrical and which symmetries they have. This is a worthwhile
investigation in itself. (The capital letter ‘B’ often has a smaller top than bottom. Here we have
assumed that they are exactly the same.)


Page 6/Our reflection
Emily’s face has been distorted by turning her mouth and eyes only through 180°.
We continue to read the smile as correct. The result is known as the Thompson effect.


Page 7/Rotational symmetry
Please e-mail for a solution.

Pages 8 and 9/Labyrinth of Lanes
Please e-mail for a solution.

Page 10/Space shuttles
Consider a 3-hour journey from Xertes to Zenon. When shuttle A starts at Xertes, shuttle 4 is
leaving Zenon. So A will see shuttle 1 as it takes off, pass 5 shuttles (nos 2,3,4,5,6) en route
and see shuttle 7 taking off as A arrives on Zenon.

Considering similar journeys leads us to conjecture that n shuttles are passed en route during
a journey of 1-2(n + 1) hours. Hence, if Astral passes 55 shuttles en route, her journey time
must be 28 hours.

Page 10 and 11/House of Wisdom
Shabakah (Gelosia)
(A) 800
(B) 238
(C) 2583
(D) 48910
(E) 17296
(F) 8736

Casting out nines
(G) Correct
(H) NOT correct
(I) Correct
(J) NOT correct
(K) Correct

Pages 12 and 13/Sam gets tessellated
Will it tessellate?
There are 9 polygons. The circle, semi-circle and oval aren't polygons. The shapes that can tile
without gaps are trapezium (turn alternate ones 180°), triangle, hexagon, kite, parallelogram and
square.

Pages 14 and 15/Are you puzzled?
Left or right?
(A) right hand (B) left hand (C) right hand
(D) left hand (E) left hand (F) right hand
(G) left hand (H) left hand (I) right hand
(J) right hand

Can you draw these?
Only one one (cross on rectangle) cannot be drawn without lifting your pencil or retracing your path.

Find twenty-five 25s
There are at least twenty-seven 25s.

Six for Twister
The remaining 6 were one eighth of the original group, which was 48.

Carol's coins
Please e-mail for solution.

Page 16 (back cover)/Winning Tickets
If the conditions for a prize were those of Mr Jones there would be 271 prize winners.

– 100 ticket holders from 300 to 399 would all win a prize; and – 171 (19 x 9) ticket holders
from 1 to 299 and 400 to 1000 would also win a prize because in every hundred there are
10 numbers with 3 in the ‘units’ place and 10 numbers with 3 in the ‘tens’ place – but don’t
count 033 twice!

There are no extra prize-winners with the amended conditions announced by the deputy-head
because every holder of a ticket with 3 on it has already been counted. However, those people
with two 3’s (28 tickets) will get an extra prize and the person with 333 will get three prizes.
That’s an extra 29 prizes giving a total of 300 altogether. TOP.



CIRCA 18: Solutions

Front cover/Alien steps
The answer to 5 up, 3 down each with 2 steps left over is 17 stairs.

Pages 2 and 3/Pirate positions
(1) Polly Parrot is A
(2) Red Rob is C
(3) The sherry is C
(4) The treasure is buried under A (palm trees)
(5) The rubies are in chest A
(6) The Black Dog is D

Pages 4 and 5/Where on Earth am I?
No solutions.


Page 6 and 7/Murder at (3,7)
The incident occurred at (3,7).

Detective Darrell was at (6,2) when the incident occurred.

Darrell first saw the accused at (6,5).

The arrest took place at (8,3).

The distance Darrell walked was 11 blocks.

The shortest distance from the incident to the place of arrest is 9 blocks.

Pages 8 and 9/Maze of nines
Please e-mail for a solution.

Pages 10 and 11/Counting up to 60 on your hands
The hands show the following: (A) 27 (B) 40 (C) 59 (D) 21

Tick Question
02;33;00
Be wary of using a calculator because any decimals will need to be translated as fractions
of 60, not 10.

Pages 12 and 13/Chinese chains
All the numbers on the island can escape.

Pages 14 and 15/Are you puzzled?
Maureen’s marbles
The marbles are distributed as follows:

Octagon: 46 marbles
Circle: 48 marbles
Triangle: 29 marbles
Square: 57 marbles
Outside: 15 marbles
Total: 123 marbles

Fifth one out!
Number 3 will become class captain.

If Dana wants to make herself the class captain, she should start counting at number 8.

What happens in circles of different numbers of class mates?

Kilo count
Sam is 5 kilos heavier than Sunita.


Poon’s plant
On the tenth day there would be
2560 flowers.

Day 1 = 5 flowers
Day 2 = 10 flowers
Day 3 = 20 flowers
Day 4 = 40 flowers
Day 5 = 80 flowers
Day 6 = 160 flowers
Day 7 = 320 flowers
Day 8 = 640 flowers
Day 9 = 1280 flowers
Day 10 = 2560 flowers

What if the plant produced 3 flowers on day 1?
Or 4 flowers? Or...?

Pages 16 (back cover)/The Frying-Plaice
Fish and chips costs £2.00 and sausage and chips costs £3.00
How to work it out:

From the first meal, there are many possibilities for 3 (fish) + 2 (sausages)
for example:
3(£1:00) + 2(£4:50) = £12:00
3(£2:00) + 2(£3:00) = £12:00
3(£3:00) + 2(£1:50) = £12:00

From the second meal, only the second of these combinations could work:
2(£2:00) + 3(£3:00) = £13:00 TOP.