If the liar says 'All my hats are green' then the statement 'All my hats are green' is false. Therefore, it is not true that all of the liar's hats are green. Given that he always lies, at least one of his hats must not be green. This implies that the liar must either have some hats or no hats at all. If he has no hats, the statement is vacuously true, which contradicts his nature as a liar.
To clarify further, if the liar has no hats, then claiming 'All my hats are green' would mean the statement is true but vacuous, which contradicts the premise that he always lies. Hence, we can conclude that he must have at least one hat to maintain his lying nature.
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