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Puzzle 1
My BrainBashers electronic world atlas has developed another fault.
I listed five countries, and how far away each was from England, and here are the results:
Australia 500 miles
Peru 8,000 miles
India 4,500 miles
Scotland 9,500 miles
France ? miles
The head weighs 24 pounds, the body weighs 32 pounds, and the tail weighs 8 pounds.
Reasoning
The trout is made up of the head, body and tail, H, B and T.
We are told that:
T = 8
(1) H = T + B ÷ 2
(2) B = H + T
Placing T into (1) and (2) we get:
(3) H = 8 + B ÷ 2
(4) B = H + 8
Using (4) in (3) we get:
H = 8 + B ÷ 2
(5) H = 8 + (H + 8) ÷ 2
Multiplying (5) by 2 we get:
2H = 16 + H + 8
2H = 24 + H
H = 24
Therefore, by (2):
B = H + T
B = 24 + 8
B = 32
Giving:
H = 24 B = 32 T = 8
And a total of 24 + 32 + 8 = 64 pounds.
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Puzzle 3
During the recent BrainBashers cipher convention, a binary code contest took place.
The contest consisted of a binary code transmission where the spaces between the letters were missing and there was no punctuation.
Each letter of the alphabet was translated into its binary equivalent based on its position in the alphabet. The resulting code was then blocked in groups of five digits.
a=1, b=10, c=11, d=100, e=101, f=110, g=111, h=1000, i=1001, j=1010, k=1011, l=1100, m=1101, n=1110, o=1111, p=10000, q=10001, r=10010, s=10011, t=10100, u=10101, v=10110, w=10111, x=11000, y=11001, z=11010
The second group of trainee astronauts are all sitting around the rectangular table, waiting to start their first day of training.
From the clues given below, can work out where everyone sits?
The seats are numbered clockwise, with Seat 1 next to Seats 2 and 8. Opposite pairs are Seats 1 & 5, 2 & 8, 3 & 7, and 4 & 6.
Harvey has a higher seat number than Jennie. Peter is across from Harvey. Neither Joyce nor Lia is in seat 8. Rick is across from Kenny, and Rick is also next to Joyce. Lia is next to Kenny. Jennie is at Seat 4 and next to Harvey. Peter is next to Lia. Mark has the remaining seat.