Puzzle 1
What is the smallest positive integer, which, when multiplied by 6 …
… gives a number consisting of only 8's?
Puzzle Copyright © Kevin Stone
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Hint
Try working backwards.
Answer
148.
148 x 6 = 888.
The easiest way is to divide successive 8's by 6 until you get an integer:
8 ÷ 6 = 1.3333
88 ÷ 6 = 14.666
888 ÷ 6 = 148
Puzzle 2
What number is …
… three-quarters of eight-ninths of one-half of 2001?
Puzzle Copyright © Kevin Stone
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Hint
Can the fractions be simplified?
Answer
667.
Reasoning
3 8 1
— of — of — of 2001
4 9 2
which simplifies to:
24
—— of 2001
72
which simplifies to:
1
— of 2001
3
Giving 667.
Puzzle 3
Which is larger:
seconds in a day
hours in 10 years
Puzzle Copyright © Kevin Stone
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Hint
Do leap years make a difference?
Answer
Hours in 10 years.
Reasoning
In a day, there are 60 x 60 x 24 seconds = 86,400 seconds.
In 10 years, there are 10 x 365 x 24 hours = 87,600 hours, which even without the leap years is already the larger number.
