Puzzle 829
Customer services at BrainBashers headquarters received the following letter recently.
Luckily, our top puzzle solvers were able to determine the meaning and help Sam South.
Can you work out what the problem was?
D-a- K-v-n,
- ---ld l-k- -- c-m-la-n ab--- -h- --- --- -f m- ----------.
-h-s- l-----s d- n-- a---a- -- b- ---k-ng c----c-l-.
As --- can s--, -h-- a-- m-ss-ng f--m -h-s d-c-m-n-.
- ---ld b- v--- g-a--f-l -f --- c--ld c----c- -h-s ---bl-m -mm-d-a--l-.
K-nd --ga-ds.
Sam S---h.
Puzzle Copyright © Kevin Stone
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Hint
Which letters are missing?
Answer
The letter was written on a typewriter that has a problem with the top row of letters printing correctly. The letter should have read:
Dear Kevin,
I would like to complain about the top row of my typewriter.
These letters do not appear to be working correctly.
As you can see, they are missing from this document.
I would be very grateful if you could correct this problem immediately.
Kind regards.
Sam South.
Puzzle 830
Can you find the country hidden in the following sentence:
Alex's aches and pains felt worse because of swollen glands that had flared up during the night, perhaps a tonic would help?
Puzzle Copyright © Kevin Stone
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Hint
The country spans more than one word.
Answer
England.
Alex's aches and pains felt worse because of swollEN GLANDs that had flared up during the night, perhaps a tonic would help?
Puzzle 831
A trout's tail weighs eight pounds.
Its head weighs as much as the tail and one-half of the body combined, and the body weighs as much as the head and tail combined.
What does the whole trout weigh?
Puzzle Copyright © Kevin Stone
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Hint
A little bit of algebra might help.
Answer
64 pounds.
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.
Puzzle 832
During a recent BrainBashers race meeting, the fastest driver managed to complete a lap with an average speed of 150 mph.
They managed to complete the first two fifths of the lap at a speed of 123 mph and the second two fifths of the lap at a speed of 164 mph.
At what speed was the final one fifth of the lap length covered?
The answer is not 176 mph.
Puzzle Copyright © Kevin Stone
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Hint
Adding the speeds won't work.
Answer
205 mph.
Reasoning
If we take the number of miles in a lap to be L miles and use Time = Distance ÷ Speed.
The first 2/5 are covered at 123 mph. Therefore, the time taken was [(2/5) x L] ÷ 123 hours.
The next 2/5 are covered at 164 mph. Therefore, the time taken was [(2/5) x L] ÷ 164 hours.
The last 1/5 is covered at y mph. Therefore, the time taken was [(1/5) x L] ÷ y hours.
The entire trip is covered at an average of 150 mph, and we can conclude that:
2L 2L L L
————— + ————— + ——— = ———
5x123 5x164 5y 150
Rearranging and simplifying gives:
1 1 2 2
——— = —— - ——— - ———
y 30 123 164
That means that y = 1 ÷ (1/30 − 2/123 − 2/164)
Using a calculator gives y = 205.
