Welcome to CIRCA

Front cover/Robot differences

(1) antenna
(2) eye red
(3) antenna has a white centre
(4) mouth turned down
(5) triangle not reversed
(6) button missing
(7) triangle not reversed
(8) triangle missing
(9) triangles reversed vertically
(10) rivet has moved

Pages 2 and 3/Testing triangles

Three types of angle
Zug: acute, Zap: right angle, Zig: obtuse

Triangle test
A correct solution
spells out CADET.

Pages 4 and 5/Revision day

1. a, 2. n, 3. g, 4. l, 5. e, 6. s

Vig’s Check Panel
If all the answers are correct the word spelt out is angles.

Pages 6 and 7/Route plot

Mission challenge
The total distance travelled by Vig is 122 km
(122.14 to be more exact).

Space Quiz
The four shapes drawn are:
equilateral triangle (M), square (T), rectangle (O) and parallelogram (A).
Rearranged, the red letters spell ATOM.

Page 8 and 9/
Which exit?
The exit that Vig
can reach is for
the 3-D Cinescreen.

Page 10 and 11/Triangle catch

The pieces that match the triangles are:
equilateral: 60° (d), 60° (d), 60° (i)
obtuse-angled scalene: 120° (y), 35° (o), 25° (u)
right-angled: 90° (g), 45° (t), 45° (e)
acute-angled scalene: 80° (t), 55° (e), 45° (h)
right-angled: 90° (l), 70° (t), 20° (o)

The letters will spell out ‘did you get the lot?’

Pages 12 and 13/Operation Earthlings
Vella is an alien and may interpret things differently from Earthlings (us!).
These are the matches: (1) e, (2) a, (3) r, (4) t, (5) h, (6) s, (7) t, (8) u, (9) d, (10) y.
It spells out ‘earth study’.)

1. Sum space journeys

(A) 9, 16, 5, 12, 4, 4
(B) 6, 27, 26, 12, 4
(C) 6, 24, 19, 11, 10, 14, 16.

2. Sum triangle

3. Who is the captain?
The captain is Alien 3. This is why:

... if Alien 1 is telling the truth then Aliens 2 and 3 are lying. We are told that there are two truth tellers, so
Alien 1 must be lying and his statement that he is the captain is untrue. Alien 3’s statement, which is true,
rules out Alien 2 as captain, so, Alien 3 must be the captain.

4. Three sums
Here are three ways to do it:
192, 384, 576
219, 438, 657
327, 654, 981

Page 15/How many?
Three differently coloured triangles can be arranged in 6 different ways.
RYG, RGY, YRG, YGR, GRY, GYR

If you use factorials, as described in Some Solutions on page 15 of the magazine, you can work out:
Four differently coloured triangles: 24
Five differently coloured triangles: 120
Six differently coloured triangles: 720

This is a permutation problem. We often get confused about the difference between permutations and
combinations. In everyday speech this doesn’t really matter (a linear combination lock is really a
permutation lock – see below). In mathematics the distinction is important.

A combination is a selection from a set where the order is not important. A permutation is an arrangement
made from a set where the order is important (in a combination lock you have to put a set of numbers in a
particular order, hence, it should properly be called a ‘permutation’ lock.