Puzzle 1
Can you find a five-digit number that …
… if you place a 9 at the beginning is four times larger than if you place a 9 at the end instead?
Puzzle Copyright © Kevin Stone
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Hint
Adding 900,000 to the numbner is the same as placing a 9 at the beginning.
Answer
23,076.
Reasoning
Placing the 9 at the beginning is equivalent to adding 900,000 (for example, 12,345 + 900,000 becomes 912,345).
Placing the 9 at the end is equivalent to multiplying by 10 and adding 9 (for example, 12,345 x 10 + 9 becomes 123,459).
Let's call the unknown number k, and we know that one of these numbers is 4 times the other, so:
k + 900,000 = 4 x (10k + 9)
k + 900,000 = 40k + 36
900,000 − 36 = 40k − k
899,964 = 39k
899,964 ÷ 39 = k
Therefore, k = 23,076.
Double-Checking
9 23,076 = 4 x 230,769 .
Puzzle 2
Can you find a word starting with BR …
… that with the addition of the letter E becomes another word that sounds the same as the first?
Puzzle Copyright © Kevin Stone
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Hint
There are at least two different answers.
Answer
BRAKING becomes BREAKING
or
BROWS becomes BROWSE
Puzzle 3
Which is larger:
millimetres in a mile
sixteenths of an inch in 2 kilometres
Puzzle Copyright © Kevin Stone
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Answer
Millimetres in a mile.
Reasoning
One inch = 25.4mm.
So:
1 mile = 1760 yards = 1760 x 3 feet = 1760 x 3 x 12 inches = 1760 x 3 x 12 x 25.4 millimetres = 1,609,344 mm in 1 mile.
And:
2 kilometres = 2000 metres = 2000 x 100 centimetre = 2000 x 100 x 10 millimetres = 2000 x 100 x 10 ÷ 25.4 inches = 2000 x 100 x 10 ÷ 25.4 x 16 = sixteenths of an inch ≈ 1,259,843 sixteenths of an inch in 2 kilometres.
Puzzle 4
Which word, if pronounced right, is wrong, but …
… if pronounced wrong is right?
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Hint
The answer is in the question.
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