Crossword Genius

Counter a graduate’s short, cross word (6)

Ross

I believe the answer is:

abacus

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'counter' is the definition.
(I've seen this before)

'a graduate's short cross word' is the wordplay.
'graduate' becomes 'ba'.
'short' suggests taking the first letters.
'word' becomes 'us' (I can't explain this - if you can you should believe this answer much more).
The initial letter of 'cross' is 'c'.
'a'+'ba'+'c'+'us'='ABACUS'

Can you help me to learn more?

(Other definitions for abacus that I've seen before include "As a cub (anag)" , "this adds up" , "It will support the architrave" , "Early counting-frame" , "that one can count on" .)

I've seen this clue in The Hindu.
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