Puzzle 6
Can you find the country hidden in the following sentence:
During the recent BrainBashers aquatic contest, the walrus struggled to finish, the sea lion finished second, and the penguin easily won!
Puzzle Copyright © Kevin Stone
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Hint
The country spans more than one word.
Answer
Guinea.
During the recent BrainBashers aquatic contest, the walrus struggled to finish, the sea lion finished second, and the penGUIN EAsily won!
Puzzle 7
I was having trouble sleeping last night and I tossed and turned well into the night.
Our local town hall has a clock which strikes on the hour and also strikes just once on the half hour.
During one of my more awake moments I heard the clock strike once, but I could not tell what time it was.
Half an hour later it struck once again, but I still could not tell what time it was.
Finally, half an hour later it struck once again, and I knew what the time was.
What time was it?
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Hint
When does the clock strike just once?
Answer
1.30 in the morning.
The initial single strike was at 12.30.
Puzzle 8
Can you find three consecutive odd numbers that …
… total 1,287 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
There are two different methods, one involves a cube root, and the other doesn't require a calculator.
Answer
9 x 11 x 13.
Reasoning #1
We're after three numbers that multiply together, so a good place to start is the cube root of 1,287, which is roughly 10.88.
Let's try dividing by the closest odd number to 10.88:
1287 ÷ 11 = 117
We're now after whole divisors of 117. Trying the odd numbers either side of 11 might work.
Trying either 9 or 13 gives the answer:
9 x 11 x 13 = 1,287
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.
Reasoning #2
We after three numbers that multiply together, but none of these can end in 5 (otherwise our answer would end in 0 or 5).
So, they can only end in 7, 9, 1 (e.g. 87, 89, 91), or 9, 1, 3 (e.g. 89, 91, 93).
However, if they ended in 7, 9, 1, the answer would end in 3 (because 7 x 9 x 1 = 63).
Therefore, they end in 9, 1, and 3 (because 9 x 1 x 3 = 27).
The first numbers we can try are 9, 11, 13:
= 9 x 11 x 13
= 99 x 13
= 100 x 13 − 13
= 1300 − 13
= 1,287
A calculator is not required!
