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Puzzle 149
If you are running in a marathon, and you overtake the person in last place …
Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.
The next highest prime number is 59:
190,747 ÷ 59 = 3,233
Let's try the next prime number, which is 61:
3,233 ÷ 61 = 53
53, 59, and 61, are all prime, and are consecutive, so this is the answer.
Double-Checking 53 x 59 x 61 = 190,747
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Puzzle 152
Frankie the Squirrel can find one acorn in 15 minutes and Glenn the Squirrel can find one acorn in 12 minutes. As autumn approaches, they both work all day and all night.
However, Alex the Squirrel is eating their collection! It takes Alex 20 minutes to eat an acorn, and Alex eats all day and all night long (and starts on yesterday's acorns).
How many extra acorns will there be at the end of a 24-hour day?
Reasoning
Frankie finds 4 acorns every hour, Glenn finds 5 acorns every hour and Alex eats 3 acorns every hour, so the nett total per hour is 4 + 5 − 3 = 6.
It is now four years since I first asked for support, and I would like to sincerely thank everyone who has helped me. BrainBashers doesn't show adverts, and I continue to depend on the ongoing support from everyone who enjoys the site.
