     © Juliet & Charles Snape 2010
Volume 16
CIRCA 46: Solutions Front cover/Reflection differences

From the left:
(1) spear pointing in
wrong direction,

(2) lightning arrows partly hidden by
eagle wings because the wings have
flipped,

(3) soldier’s arms and spear have
switched sides,

(4) head facing in wrong direction,

(5) top lightning arrows wrong.

Pages 2 and 3/A symmetrical soldier

Pages 4 and 5/Missing tiles

Pages 6 and 7/
Shopping in the sitting

Ophelia spent exactly 2 denarii. This is how:
Olives 4 as (L),
Togas 12 as (A),
Clay pot 8 as (I),
Honey 2 as (N).

This makes a total of 32 as
or 2 danarii. The letters spell out Latin, the language of the Romans.

Page 8 and 9/Multiples maze Page 10 and 11/Chariot race puzzle

The results are:
1st Green driven by Quickius.
2nd White driven by Axis.
3rd Red driven by Fastius.
4th Blue driven by Speedius.

Clue 4 is critical to cracking the puzzle. Because we know that Axis can’t be in first place (see Clue 3)
then he must be second and thus the third placed chariot is red (see Clue 1).
Page 14 and 15/Are you puzzled? Page 12 and 13/Roman time traveller

1. It has rotational symmetry. m
2. It has rotational symmetry of the order eight. o
3. It has two lines of reflective symmetry. s
4. It has one line of symmetry. a
5. The blank triangle has three lines of symmetry. i
6. It has planes of symmetry. c
1. Twin shields
The two identical shields are
6 and 10.

2. Triangle count
There are 13 triangles.

3. Romans in a line
From the left: Abacus, Claudius, Damus, Brutus.

4. Finish the mosaic

5. What's next?
21 (the next number is made by summing the previous two numbers) and
127 (the next number is double the previous difference).

6. Find the numbers  Alice: Maths in Margate (back page)
The smallest number of coins Uncle Ben could have found is 14.

(3 x 4 = ) 12 + 2 =14
(5 x 2 = ) 10 + 4 = 14
Page 15/Number surprise
No matter how large a number is multiplied by 6 the product will always reduce to 3, 6 or 9.
(This reduction is called the digital root.)
This numbers will continue to be cycled through 6, 3, 9 , 6, 3, 9, ...

Other times tables explored in the same way produce some surprising results.

9 x 1 = 9
9 x 2 = 18 1 + 8 = 9
9 x 3 = 27 2 + 7 = 9

or

8 x 1 = 8
8 x 2 = 16 1 + 6 = 7
8 x 3 = 24 2 + 4 = 6
8 x 4 = 32 3 + 2 = 5        