Puzzle 750
Can you find three consecutive even numbers that …
… total 85,008 when multiplied together?
Puzzle Copyright © Kevin Stone
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Hint
Try starting with the cube root of the number.
Answer
42, 44, and 46.
Reasoning
As we require 3 numbers that are multiplied together, we can start with the cube root of 85,008 ≈ 43.97.
We can now check that 44 divides 85,008 exactly: 85,008 ÷ 44 = 1,932, which means that 44 is likely to be one of the numbers.
And as we know that we need consecutive even numbers, we soon find 42 and 46 as the remaining numbers.
Double-Checking
42 x 44 x 46 = 85,008.
Puzzle 751
Which is larger:
fathoms in a kilometre
hours in a month
Puzzle Copyright © Kevin Stone
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Answer
Hours in a month.
Reasoning
A fathom is 6 feet, which is 1.8288 metres.
So there are 1000 ÷ 1.8288 ≈ 546.8 fathoms in a kilometre.
The shortest month has 28 x 24 hours = 672.
So even the shortest month has more hours than there are fathoms in a kilometre.
