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?
Answer
In the phrase 'my bucket and your spade', the gap between 'my' and 'and' is the same as the gap between 'and' and 'spade', namely one word.
Indeed, this logic can be continued to give the following sentence. In the first sentence the gap between 'and and' and 'and and' is seven words, et cetera.
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Puzzle 19
Using a tap, a nine gallon container and a four gallon container …
Hint
Start by filling the 9 gallon container, and then use that to fill the 4 gallon container.
Answer
Here are the contents of the containers after each stage:
A B
9 0 fill A
5 4 fill B from A
5 0 empty B
1 4 fill B from A
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A
6 0 empty B
This leaves 6 gallons in container A.
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Puzzle 20
Can you find every occurrence of the word JUNE that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
