(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

particular solution please e-mail).

on right and bottom row, third on right.

(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.

No solutions.

A solution is given on page 14 of the magazine (CIRCA 16).

There are four different routes that lead to a successful exit. Requires visual solution.

Please e-mail.

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

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

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.

See page 14 of the magazine (CIRCA 17).

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.)

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.

Please e-mail for a solution.

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.

(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

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.

(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.

– 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.

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

(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

No solutions.

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.

Please e-mail for a solution.

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.

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...?

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.