Puzzle 201
Can you find the country hidden in the following paragraph:
The local habitat around a railway track can be very interesting. For example, supporting the track is a sleeper, under which you can find the lesser-spotted great weevil.
Puzzle Copyright © Kevin Stone
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Hint
The country spans more than one word.
Answer
Peru.
The local habitat around a railway track can be very interesting. For example, supporting the track is a sleePER, U nder which you can find the lesser-spotted great weevil.
Puzzle 202
If you are running in a marathon, and you overtake the person in last place …
… what position are you now in?
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Hint
Who is in last place?
Answer
This cannot happen, you cannot overtake the person who is in last place, as there is no-one behind them!
Ovetaking = passing someone who is ahead on the same lap, this is a change of position, e.g. 4th moves up to 3rd .
Lapping = passing someone who is a full lap behind, this isn't a change of position, e.g. 4th stays 4th .
Puzzle 203
Can you find three consecutive odd numbers that …
… total 7,644,585 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
195 x 197 x 199.
Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.
Let's try dividing by the closest odd number to 196.99:
7644585 ÷ 197 = 38805
We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.
Trying either 195 or 199 gives the answer.
Double-Checking
195 x 197 x 199 = 7,644,585
Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Puzzle 204
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.
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