Pages 12 and 13/Ice screamer
Paula’s position in the queue reduces by two each time someone is served, the person served
plus the person pushed by. Children should therefore discover that the number served before
Paula makes it to the front is 15. For all such queues with the same conditions (i.e. an even
number in the queue) the result will be half the queue. Where the queue is an odd number of
people then it’s the highest multiple of 2, e.g. 31 in queue and 15 people served before Paula
gets to front.
Pages 14 and 15/Are you puzzled?
Pinboard puzzles
1. A 2. B 3. A 4. B
Divide the lot!
1 (2–3 of 3–4 = 1–2 + 1–2 = 1).
Find the spy
The spy is, starting from the top left: row 4, column 6.
How many?
12 chocolates..
Which is next?
Each symbol is made by using a numeral and its reflection.
The line of numbers is 1, 2, 3, and 4; the next in line is 5, the first of the designs.
Twice as much
The one-eyed alien must give 10 dollars to the three-eyed alien.
The one-eyed alien will then have 20 dollars and the three-eyed alien will have 40 dollars.
Page 16 (back cover)/Counting time
Number of lines:
1 = 2, 2 = 5, 3 = 5, 4 = 4, 5 = 5, 6 = 6, 7 = 3, 8 = 7, 9 = 6, 0 = 6
Poona brought the food over to Alice at 17:48 (12 minutes to 6 pm).
After 30 minutes the time was 18:18 (18 minutes past 6 pm).
The time of day with most lines 08:08 (8 minutes past 8 am). It uses 28 lines.
The time of day using the least number of lines is 11:11
(11 minutes past 11 am). It uses only 8 lines.
TOP.
CIRCA 24: Solutions
Front cover/Achilles mirror image
The mirror image is number 6. (1. strap missing on front leg;
2. belt missing; 3. sandal leathers reduced; 4. head-band missing;
5. money bag missing; 7. bracelet missing; 8. leg straps missing;
9. finger not pointing.)
Pages 2 and 3/Highway robbery?
(A) Route 1 (100 km): Swan Inn to Castle Town (26 km) to Ports Town (24 km) to
Crossways (26 km) to Windy Hill (16 km) back to the Swan Inn (8 km).
Route 2 (takes 11 hours at 10 km per hour; 110 km): Swan Inn to Marsh Point (40 km) to
Lighthouse Point (6 km) to Ports Town (14 km) to Castle Town (24 km) back to
the Swan Inn (26 km).
Route 3 (takes 12 hours at 10 km per hour; 120 km): Swan Inn to Marsh Point (40 km)
to Lighthouse Point (6 km) to Ports Town (14 km) to Castle Town (24 km) to
Crossways (12 km) to Windy Hill (16 km) back to the Swan Inn (8 km).
(B) Bad Bob never gets to rob the mail coach. None of the routes can go along the road between
Castle Town and Marsh Point in this puzzle as the route would result in an odd number of
kilometres travelled and all the routes have an even total.
Pages 4 and 5/Measuring Greeks
There could be some arguments about which measure matches which item but, by elimination,
children should arrive at the following ‘agora shopping list’:
rope M fathoms
cloth A cubits
belt R feet
cabbage K span
figure E palms
nails T digits
The mystery word is ‘MARKET’.
The drawing of the ‘Measuring man’ is based on the ‘Metrological Relief’ that can be found at
the Ashmolean Museum in Oxford. The table shows the more common measurements of
ancient Greece. The ‘Metrological Relief’ shows measurements that are local to the part of
Greece in which it was carved and are slightly different.
Page 6 and 7/Colossus
This spread links up with ‘Measuring Greeks’ on page 5, which provides a table with
cm equivalents and a full-size photograph of a man’s hand to measure.
The discovery that the width of one’s own thumb is the same as its length leads on to knowing
the length of the statue’s thumb’s length because we know it was the equivalent of a fathom
(a man could just reach around it). The table on page 5 tells us that a fathom was 177.6 cms.
The photograph on page 5 can be used to measure how many times a digit (the width of the
middle finger) goes into a thumb,either with a ruler or a marked piece of paper.
Having agreed with an estimate of 4 times, the width of Colossus’ finger can be worked out by
dividing 177.6 by 4.
This gives us Colossus’ equivalent of a Greek digit as 44.4 cms.
Using the information in the table on page 5:
One Greek foot equals 14 digits,
so, Colossus’ foot is 44.4 x 14 = 621.6 cms
One Greek fathom equals 6 feet,
so, Colossus’ equivalent of a fathom is 621.6 x 6 = 3729.6 cms
Both the cartoon on page 7 and the illustration by Leonardo on the worksheet illustrates that
a fathom is the same length as a man’s height, giving us the height of 37.30 metres
(122 ft) for the statue of Colossus. (This does not include the height of the plinth.)
Alternatively, pupils can use ratios of their thumb length to their height to compare
Colossus’ thumb and height.
A nice extension to this activity is to get the child to work out how tall a statue of themselves
would be if it was built to the same scale as Colossus.
See also ratio and estimating Mona Lisa’s height in CIRCA, Issue 21, Volume 7.
Pages 8 and 9/Something for nothing
Achilles started with 6 coins in his pocket.
At finish of first run 6 x 2 = 12
After paying old man 12 – 8 = 4
At finish of second run 4 x 2 = 8
After paying old man 8 – 8 = 0
(In case you didn’t notice, the secret words are an old saying ‘A fool and his money are
soon parted’ spelt backwards.).
Pages 10 and 11/Time matches
A 5 180° 18.00
B 6 45° 19.30
C 4 120° 8.00
D 1 60° 22.00
E 3 30° 13.00
F 2 90° 15.00 .
Pages 12 and 13/Tara’s T-shirt
jam 4 9 36
gum 1 9 9
gravy 2 9 18
ice cream 5 9 45
chocolate 3 9 27
custard 6 9 54
Total 21 189
Tara’s nan has enough ‘Stain Buster’; there will be 11ml left in the bottle.
Pages 14 and 15/Are you puzzled?
Missing middle
The missing number is 381. In each row the middle number (median) is halfway between
those on either side.
Bad Bob’s missing bit
The missing bit of hat is 3.
Pencil place
(I) is the longest and (G) is the shortest.
In order, longest first,
(I) 160mm,
(F) 147mm,
(A) 142mm,
(E) 130mm,
(D) 124mm,
(C) 120mm,
(B) 115mm,
(J) 111mm,
(H) 105mm,
(G) 100mm.
Little or large
It’s relative!
Around the palace
Please e-mail for a solution.
End-to-end
Please e-mail for a solution.
Pages 16 (back cover)/Air time
Alice is right, although it’ll be an early breakfast as Nick will be landing 03.00 on Thursday. TOP.