A million grains of sand is a heap. If we remove one grain of sand from this heap, we will still have a heap.
We can now keep repeating (2) until we only have a single grain of sand remaining.
Is this a heap? Clearly not. But what went wrong with our thinking?
This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer.
Both (1) and (2) are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. If we remove one more grain, we're left with nothing, is this still a heap?
Hint
It doesn't actually matter how many men or women there were.
Answer
17,760 dollars.
If there were M men, then there were (3552 − M) women.
So one ninth of the men each received 45 dollars and one twelve of the women each received 60 dollars. So the total received was:
= 45 x 1 x M + 60 x 1 x (3552 − M)
— ——
9 12
Simplify the two fractions by dividing the 45 by 9, and the 60 by 12 respectively.
= 5 x M + 5 x (3552 − M)
= 5M + 17760 − 5M
= 17760
?
Puzzle 484
Which is larger:
millimetres in a milesixteenths of an inch in 2 kilometres
1 mile = 1760 yards = 1760 x 3 feet = 1760 x 3 x 12 inches = 1760 x 3 x 12 x 25.4 millimetres = 1,609,344mm 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.
