     © Juliet & Charles Snape 2009
Volume 14

CIRCA 40: Solutions

Front cover/Balloon twins:
The two matching balloons are: top row, fifth from left and bottom row, second from left..

Pages 2 and 3/Penny primes
Factor chart
2
(prime), 3 (prime), 4 (2), 5 (prime), 6 (2,3), 7 (prime), 8 (2,4), 9 (3), 10 (2,5), 11 (prime), 12 (2,3,4,6),
13
(prime), 14 (2,7), 15 (3,5), 16 (2,4,8), 17 (prime), 18 (2,3,6,9), 19 (prime), 20 (2,4,5,10), 21 (3,7),
22 (2,11), 23 (prime), 24 (2,3,4,6,8,12), 25 (5)

You could try to make penny piles for each number over 25 but this would a long time. The best way
to go about it is by taking out all even numbers (they will all make piles of 2), then take out all the
numbers that are multiples of 3 (they will all make equal piles of 3) and the same with 5. After this you
take out multiples of 7 (they will make equal pile of 7) and so on with each higher prime you find.
This method was invented by a Greek mathematician over 2000 years ago. It's call the 'Sieve of Eratosthenes'

Pages 4 and 5/
Backwards and forwards
All 2-digit numbers eventually become palindromes (89 or 98 takes 24 stages). If you organise your
work you might have discovered that starting numbers whose two digits sum to less than 10 always
become palindromes after the first stage. You may also have found out that all the palindromes are
divisible by 11.

If you go on to investigate 3- and 4-digit numbers. Be aware that the number 196, even though it has
been taken to a number with over 10 million digits, has not yet become a palindrome.

A train problem
At 2:15 pm the trains were 15 minutes apart. So, travelling at the same speed they would pass each
other seven and half minutes later at twenty two and a half minutes past two.

Page 6 and 7/Exploring prime numbers
Primes and sixes

29 - 23 = 6, 37 - 31 = 6, 53 - 47 = 6, 59 - 53 = 6,
67 - 61 = 6, 79 - 73 = 6, 89 - 83 = 6

Prime twin pairs
3,5 5,7 11,13 17,19 29,31 41,43 59,61 71,73
You may notice that, with the exception of (3,5) the numbers between the pairs are multiples of 3.
Note that (2,3) are also considered to be a prime twin pair.

Prime sums
4 is 2 + 2
6 is 3 + 3
8 is 3 + 5
10 is 3 + 7
12 is 5 + 7
14 is 7 + 7
16 is 5 + 11
18 is 7 + 11
20 is 3 + 17
22 is 5 + 17
24 is 7 + 17
26 is 7 + 19
28 is 11 + 17
30 is 11 + 19
32 is 13 + 19
34 is 11 + 23
36 is 13 + 23
38 is 7 + 31
40 is 3 + 37
42 is 5 + 37
44 is 7 + 37
46 is 5 + 41
48 is 7 + 41
50 is 7 + 43
52 is 5 + 47
54 is 7 + 47
56 is 3 + 53
58 is 5 + 53
60 is 7 + 53
62 is 3 + 59
64 is 5 + 59
66 is 7 + 59
68 is 7 + 61
70 is 3 + 67
72 is 5 + 67
74 is 7 + 67
76 is 5 + 71
78 is 7 + 71
80 is 7 + 73
82 is 3 + 79
84 is 5 + 79
86 is 7 + 79
88 is 5 + 83
90 is 7 + 83
92 is 3 + 89
94 is 5 + 89
96 is 7 + 89
98 is 19 + 79
100 is 3 + 97

There are other ways

Page 8 and 9/
Primes underground

4. Face the sum
1442 + 423 = 1865

5. Eggless
The Queen bought 12 eggs.

6. Arrows
7 x 6 ÷ 7 x 4 = 24 9 ÷ 3 x 10 ÷ 6 = 5 (Several answers are possible.)

7. Cotted babies
The Duchess had 4 babies (and 3 cots).

Page 16 (back cover)/Who dunnit?
Mr Grey was the thief.

From the final ‘bubble’ coming from the TV we know that it wasn’t Mr Green or the man wearing
a grey coat (this has to be Mr Brown) because they were 10 miles away. This leaves Mr Grey.

TOP.   Pages 14 and 15 /Are you puzzled?

Riddle
The word spelled out is: TEACHER.

1. BC (be careful)
King Saul was born in 240 BC.

2. How old am I?
Father William is 194 years.

3. Find the differences
The differences in the pictures are: 1. price on hat changed, 2. cake and plate missing,
3. spots missing, 4. teacup missing, 5. tie missing, 6. pattern on teapot missing, 7. ivy missing,
8. Alice’s bow missing, 9. teacup missing and 10. chair leg missing
Pages 10 and 11/Tile match
The matching tiles are: Set 1 M,O Set 2 E,R Set 3 S,H Set 4 N,G Set 5 F,I
(it spells out FISHMONGER).

Ironmongers sold metal goods such as nails, screws, tools, coal shuttles, kettles and so on.
A costermonger (from old English costard meaning apple) sold fruit and vegetables usually from a stall.

Pages 12 and 13 /The omnibus puzzle 