As I was going to St Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits.
Kits, cats, sacks and wives,
How many were going to St. Ives?
This is a very old puzzle, and appeared in a manuscript dated around 1730. It is thought to refer to a town in Cornwall, UK.
If we were to count everyone and everything, including all of the kits, cats, sacks and wives, we would have:
Me = 1
Man = 1
Wifes = 7
Sacks = 7 x 7 = 49
Cats = 7 x 7 x 7 = 343
Kits = 7 x 7 x 7 x 7 = 2401
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?
