The difference between Anyone's guess and Puzzle
When used as nouns, anyone's guess means a mystery, whereas puzzle means anything that is difficult to understand or make sense of.
Puzzle is also verb with the meaning: to perplex (someone).
check bellow for the other definitions of Anyone's guess and Puzzle
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Anyone's guess as a noun (idiomatic):
A mystery; something unpredictable.
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Puzzle as a noun:
Anything that is difficult to understand or make sense of.
Examples:
"Where he went after he left the house is a puzzle."
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Puzzle as a noun:
A game for one or more people that is more or less difficult to work out or complete.
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Puzzle as a noun:
A crossword puzzle.
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Puzzle as a noun:
A jigsaw puzzle.
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Puzzle as a noun:
A riddle.
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Puzzle as a noun (archaic):
Something made with marvellous skill; something of ingenious construction.
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Puzzle as a noun:
The state of being puzzled; perplexity.
Examples:
"to be in a puzzle"
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Puzzle as a verb (transitive):
To perplex (someone).
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Puzzle as a verb (intransitive):
To think long and carefully, in bewilderment.
Examples:
"We puzzled over the curious-shaped lock, but were unable to discover how the key should be inserted."
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Puzzle as a verb (transitive):
To make intricate; to entangle.