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

Volume 9

CIRCA 25: Solutions

Front cover/Roman route: Please e-mail for solution.

Pages 2 and 3/How the Romans wrote their numbers
The correct solution spells out GLADIATOR.


Of interest
On clocks and watches using Roman numerals 4 is most often written as IIII. Two explanations
are offered; (a) it produces a more attractive face (b) they were based on the sundials of ancient
Rome. The Westminster Great Clock (often mistakingly referred to as Big Ben – the bell)
is one of the few clocks that has 4 written IV (in gothic lower case letters).

Pages 4 and 5/
What's the distance?
(1) Cavitus is the nearest.
Using the distance table you find that:
Aquarium (Molia) 60 milia passuum
Odearium (Decayius) 20 milia passuum
Eggium (Cavitus) 17 milia passuum

(2) To label the map some deduction is necessary. Again, use the distance table to find which
town is nearest Tiptopium by road. It’s Odearium. The other two towns can be identified by
finding distances from Circadium or Ohmyium using the distance table.


Milestone
1. Tiptopium 2. Odearium 3 Ohmyium 4. Tiptopium
5. Hardium 6. Aquarium 7. Caromello 8. Hardium
9. Eggium. This spells out TOOTHACHE


Page 6 and 7/Ride around
The exact measure for a mille passus (plural milia passuum) is 1.48 km.
On the conversion graph this has been rounded to 1.5 km to a mille passus.

To visit all the towns under 24 hours Speedia needs to visit Eggium first and then return
to Circadium. The journey finishes with Speedia arriving in Tiptopium, having travelled
for 23 hours 30 minutes. Here’s her route:

mp km time taken (hours)
Circadium to Eggium 17 25 2.5
Eggium to Circadium 17 25 2.5
Circadium to Hardium 10 15 1.5
Hardium to Caromello 30 45 4.5
Caromello to Ohmyium 20 30 3.0
Ohmyium to Aquarium 17 25 2.5
Aquarium to Odearium 23 35 3.5
Odearium to Tiptopium 23 35 3.5
23.5

Page 8 and 9/Which average?
(A) is the median
(B) is the mean
(C) is the mode

Questions that could be asked:
(1) was the sample too small?
(2) Which average would have been most appropriate for the statue?


Pages 10 and 11/Capture the Eagle
The rules of this version of Ludus Latrunculi are easy to learn. It is harder to capture
the Eagle than remove all the opponent’s men. The fact that the Eagle can’t be taken
makes it a powerful piece.

Further activities
Children could play on different size grids and with more counters. Ask them how this
affects the game. Is it a faster game or slower? Do they have to adopt different strategies?
Why do they think chess and draught boards are 8 x 8?

History of Ludus Latrunculi
The Romans spent a lot of time playing board games involv-ing dice or strategy.
The most popular thinking game of the times was Ludus Latrunculi. Many different board
layouts have been found such as 6 x 8, 8 x 8, and 8 x 14. In 1996, an unfinished game
using a 8 x 12 board was discovered in Essex.

Ludus Latrunculi was probably derived from the Greek game of Petteia which means pebble.
According to Plato this game had been derived from an earlier Egyptian game.

Some other games played by the Romans: Draughts (Calculi)
Noughts and crosses (Terni Lapilli) and
Backgammon (Tabula).

SPQR stands for Senatus Populusque Romamanus which translates as
‘the Senate and the People of Rome’.
As well as on standards, SPQR was used on official documents and inscriptions.

Pages 12 and 13/Gruesome graphs
(1) The chariot achieved its fastest speed in Lap 7.
(In most horse races there is a sprint for the finish.)

(2) Murder by stabbing
(by far! and includes stabbings with daggers, swords and spears).

(3) 40 defeated gladiators survived along with 50 victorious gladiators.
About 90% of all professional gladiators survived to retirement.

(4) Lottery prizes.

Pages 14 and 15/Are you puzzled?
1. Roman racers
Domius is the only charioteer to give us an actual number of races won. Domius won 16 races
(half his age). From there we can work out that Carvilos won 34 races (2 x 16) + 2; children often
miss the ‘2 more than...’). We can now work out that Brutus won 68 races and Abutius, 73 races.
So, races won: Abutius 73, Brutus 68, Carvilos 34 and Domius 16.

2. Find the pick pockets
Please e-mail for solution.

3. How old?
This puzzle is best solved using trial and improvement.
Ophelia is 6 years old..

4. Romulus and Remus
The twins are D and G.

5. Supre peach
Please e-mail for solution.

6. How many?
This problem can be solved by factorizing or trial and improvement.
7 (a prime number) is the only factor of all the three amounts of fruit.

Page 16 (back cover)/Tops for Alice
(1) Fab Tops is slightly cheaper by 30p per ‘top’ than Top of the Tops.
If only one ‘top’ was purchased Fab Tops would be cheaper by 1p.

Fab Tops: 2 tops = £30.00 ÷ 2 = £15.00 each.

Top of the Tops: 2 tops = £31.00 plus £3.00 p+p = £34.00
minus £3.40 (10% discount) = £30.60 ÷ 2 = £15.30

(2) Three ‘tops’ from Top of the Tops is cheaper (£15.63 each) than Fab Tops (£15.66). TOP.


CIRCA 26: Solutions

Front cover/What number?
There is only one way to fit the blocks together. They make the 4-digit number 6174. (See
pages 12 and 14). The puzzle can be solved by visualisation or by tracing the pieces and fitting
them together (they only fit in one way).

Information
This issue has taken the Japanese comic style ‘Manga’ as its inspiration. Manga is Japanese
for ‘Ranom sketches’.These were produced as woodcuts in the 19th century by most of Japan’s
prominant artists. These were sold as instructional manuals for amateur artists. Today, manga
style magazines and comics are big business with over 50 billion sold in Japan alone.
The kanji on the cover is the ‘comicese’ KERRANNGI!!!!, a breaking or cracking noise.

Pages 2 and 3/Numbers in Japan
There are 14 lines of 10 in the grid. It’s useful to keep a tally as each group of 10 is found.

Information
The number names for 1 to 10, 100, 1000 and 10000 are ichi, ni, san, shi, go, roki, shichi,
hachi, kyuu, juo, hyaku, sen, man. Two-digit numbers (except 10) are made by combining
e.g. ichi-juo (11), ni-hyaku roki-juo hachi (268) and so on.

More digits
(1) 658 (2) 4097

Japanese money
(A) ¥10 (B) ¥5 (C) ¥100 (D) ¥50 (E) ¥1 (F) ¥500

How much?
(a) ¥180 (b) ¥300 (c) ¥260 (d) ¥4000 (e) ¥350

Information
The exchange rate of sterling to yen: £1.00 converts to ¥185 (Spring 2004)

Pages 4 and 5/
Noodle nuts
1. (04:30) Not enough (U)
2. (07:45) 2.25 (S)
3. (10:43) 10.55 (O)
4. (11:38) 12 litres (C)
5. (12:10) ¥180 (O)
6. (14:21) ¥2151 (P)
7. (19:59) ¥237 (T)
The correct answers spell out OCTOPUS.


Page 6 and 7/Which rides
Sachiko went on each of the three 3-star rides.
(3 x ¥1500 = ¥4500 ¥5000 – ¥4500 = ¥500 left.)
Kenji went on two 3-star rides, Dead-Drop, SkyShoot (he didn’t think much of Swordfish –
see frame 1) and the 2-star Frenzy.
(2 x ¥1500 + ¥1200 = ¥4200
¥5000 – ¥4200 = ¥800 left.)
Yumie went on each of the three 1-star rides. He was the one who bought the hat.
(3 x ¥900 + ¥700 = ¥3400
¥5000 – ¥3400 = ¥1600 left.)

The problem can be solved by trial and improvement but is best answered by making a table
of all the possible combinations of rides.


Page 8 and 9/Catch
Please e-mail for a solution.

Page 10 and 11/Mathematical mats
(A) 27 mats (B) 16 mats
(C) 72 mats. There are 9 rooms, so 9 x 8 = 72.
(D) The tatami seller would make a profit of ¥172500.

Information
A tatami mat consists of three items. A thin layer of tightly woven straw (omote) which is
sewn to a thicker more coarsely packed layer (doko). The two are then hemmed with a
fringe (beri).

The size of tatami mats varied in their size from region to region; Kyou-ma 191cm x 95cm,
Chuukyou 180cm x 90 cm, Kantou-ma 176cm x 88cm. Most tatami mats produced today are
approximately 1m x 2m. There are 15 areas where rice straw is harvested and each has its
own distinct colour.

Tatami mats are hard wearing and provide very good sound proofing. The compressed straw
doesn’t catch fire very easily but if it does it won’t let off any poisonous gases.

Between 4000 and 5000 lengths of straw are used to make a single mat.

Pages 12 and 13/Curious numbers
1234 takes two stages to become 6174, 7777 becomes 0000 and 2004 takes four stages to
become 6174.

8991 of the 9000 4-digit numbers become the Kaprekar constant 6174 (1111, 2222 etc,
obviously do not).

It takes 7 or less stages for any 4-digit number (excluding the obvious) to become the
Kaprekar constant. See page 14 of Circa 26 for more on the Kaprekar constant.

Essentially, the puzzle is to find the difference between the largest number and the
smallest number which are possible from arranging any four digits.

Page 14/The curious number 6174
This interesting number provides good practise in number operations and in recording an
investigation. 3-digit numbers take a maximum of 6 stages to reach the Kaprekar constant
of 495 (3-digit numbers whose digits are all the same e.g. 444 do not become the Kaprekar
constant).

Niven numbers
236 is not a Niven number.


Pages 14 and 15/Are you puzzled?
1. Boxes of chibis
Hiako will place a box of white chibis in the space so that each row and column
contains 2 black and 2 white.

2. Noodle nuts
A bowl of noodles and prawns costs ¥40. (Noodles with chicken costs ¥20 and with
vegetables ¥30.)

3. Moving barrels
Please e-mail for a soution.

4. Corks
A cork costs ¥5. (A bottle costs ¥20 plus ¥5.)

5. Tea chests
There are 40 tea chests in the stack.

6. Fishy puzzle
He has 28 hake (33 cod and 39 sardines).

Page 16 (back cover)/A problem with sushi
Alice bought 63 pieces of sushi. Alice had seven friends round for tea.
Each had eight pieces of sushi and Alice had seven pieces.

Information: Sushi means ‘vinegared rice’. Vinegar helps preserve the
rice and aids digestion
.. TOP.


CIRCA 27: Solutions

Front cover/Crack the safe: The combination is: 6, 4, 7, 1, 2, 3, 9, 8, 5 (finish here).

Pages 2 and 3/Decimal match
(A) 0.2 (B) 0.01 (C) 0.125 (D) 0.1 (E) 0.75 (F) 0.6 (G) 0.65 (H) 0.9
.

Pages 4 and 5/
Detective De Duction
1. Split the clock
10 + 11 + 12 + 1 + 2 + 3 = 39
4 + 5 + 6 + 7 + 8 + 9 = 39


2. Seven ones
11 + 11 + 11 +1 = 34

3. Odd shadow
The shadow of the umbrella is on the wrong side of the detective.

4. Camera shot
C is the correct shot.

5. Footprint numbers
(A) double (B) add 1 (C) halve (D) add 0.5

6. Fill in the blanks
(E) 16 (F) 12 (G) 4 (H) 0.25 (I) 3.25 (J) 26

7. Picture shapes
(1) D (2) C (3) F (4) A

8. Missing jewel
B (the square emerald).

9. Which key?
(H) is the key to the padlock.

10. Name the set
Not squares.

11. Squares within squares
10 squares
.

Page 6 and 7/Know your place
(A) £12999.99 (D) 1.1 m (G) 2.45 kg
(B) 150.5 cm (E) 7.5 (H) 18.5 years
(C) 330 ml (F) 3.5 litres (I) £40.99

Page 8 and 9/Decimal trails
3 = (Signpost) 0.5 + 1.5 + 0.5 + 0.5
4 = (Signpost) 0.5 + 1.5 + 0.5 + 0.5 + 0.75 + 0.25
6 = (Signpost) 0.5 + 1.5 + 0.5 + 0.5 + 0.75 + 0.25 + 0.2 + 0.8 + 0.3 + 0.7
5 = (Signpost) 0.5 + 1.5 + 0.2 + 0.8 + 0.5 + 0.4 + 0.6 + 0.5
2 = (Signpost) 0.5 + 0.5 + 0.3 + 0.7
1 = (Signpost) 0.5 + 0.02 + 0.03 + 0.4 + 0.05


Pages 10 and 11/The dancing men
The final message from Abe Slaney was:
ELSIE PREPARE TO MEET THY GOD

The message sent by Sherlock was:
COME HERE AT ONCE

There are 18 different dancing men, standing for the letters:
A, B, C, D, E, G, H, I, L, M, N, O, P, R, S, T, V and Y.

Pages 12 and 13/Inspector Sherbert
Clue A (2) Clue B (7) Clue C (10) Clue D (15) Clue E (18) Clue F (26)

Using ‘Sherbert’s Clue Decoded’ we find that the culprit (2, 7, 10, 15, 18, 26) was JULIET.

Pages 14 and 15/Are you puzzled?
Which pair?
Combs are the only pair, all the other items are in triplicate!

Swag bags
There are 11 items in Charlie’s bag.

Police numbers
There are 959 female officers in
Middleton Police Division.

Fingerprint
Jones’ fingerprint was on the cup.

Crack this!
The message reads:

HOLMES PLAYED THE VIOLIN

Can you work out the combination?
The comination is start at 14, then,
15, 3, 4, 12, 10, 2, 1, 5, 7, 11, 9, 13, 16,
8, 6 (OPEN).

Page 16 (back cover)/Five more lengthsAlice swam five lengths of the pool on the
first day (Monday). The puzzle can be solved by reasoning, by trial and improvement
or by simple algebra: (n) + (n + 5) + (n + 10) + (n + 15) ... TOP.