Puzzle 517
Exactly how many minutes is it before eight o'clock if …
… 40 minutes ago, it was three times as many minutes past four o'clock?
Puzzle Copyright © Kevin Stone
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Hint
How many minutes are between the times?
Answer
50 minutes.
Reasoning
If we call the number of unknown minutes T.
Between four o'clock and eight o'clock, there are 240 minutes.
There is some point between these two times, before which we have 3 lots of T, and after which we have one lot of T plus 40 minutes.
Therefore, in the 240 minutes, there are 4 lots of T plus 40 minutes.
240 = 4 x T + 40.
Therefore, T = 50 minutes.
Puzzle 518
What well known saying is expressed here:
Refrain from enumerating your owned domestic fowl while their hard, porous calcium containers are undamaged.
Puzzle Copyright © Kevin Stone
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Answer
Don't count your chickens until they're hatched.
Puzzle 519
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
923,076 = 4 x 230,769.
Puzzle 520
What 5-letter word can be added to the end of these words to make new words:
green out light bird boat club cook
Puzzle Copyright © Kevin Stone
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Hint
The word begins with the letter H.
Answer
House.
To give: greenhouse, outhouse, lighthouse, birdhouse, boathouse, clubhouse, cookhouse.