## Puzzle 5

Some months have 30 days, some have 31, but how many have 28 days?

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## Puzzle 6

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?

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Hint

Who was going to St. Ives?

Answer

One.

Only I was going to St. Ives.

## Puzzle 7

How many grains of sand do you need...

...until you have a heap of sand?

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Hint

Is a million grains of sand a heap?

Answer

We can probably agree on two things:

A million grains of sand is a heap.

If we remove one grain of sand from a heap, we 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. When does the heap become a non-heap? If we remove one more grain we're left with nothing, is this still a heap?

## Puzzle 8

What always weighs the same...

...no matter how large it is?

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Hint

There are at least 4 answers that fit the question.

Answer

A hole or a vacuum, or perhaps a set of scales, or maybe a shadow.

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