Crossword Genius

Aristo saving tiny bit of cash shows intelligence (3-3)

Ross

I believe the answer is:

tip-off

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'intelligence' is the definition.
The answer and definition can be both related to thinking as well as being singular nouns.
Maybe there's an association between them I don't understand?

'aristo saving tiny bit of cash' is the wordplay.
'aristo' becomes 'toff' (I've seen this before).
'saving' means one lot of letters goes inside another.
'tiny bit of cash' becomes 'ip' (I can't justify this - if you can you should give a lot more credence to this answer).
'toff' going around 'ip' is 'TIP-OFF'.

'shows' is the link.

Can you help me to learn more?

(Other definitions for tip-off that I've seen before include "Private warning" , "Warn helpfully" , "Give advance warning or inside information" , "Piece of secret information" , "Confidential hint" .)

I've seen this clue in The Independent.
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