Card trick

This trick is well known, but it can be generalized.
Let secretly choose any card in a 21 cards pack.
Deal one card at a time in 3 rows and ask in which row is the card.
Take back the rows, letting the one said in the middle
Redo two other times the same operation
The secret card is then the 11th card !
Why ? Play

Generalizing

A 21 cards stack is not very usual, find a generalization of this trick with
- a normal stack of 32 cards Solution
- a normal stack of 52 cards. Solution
- even more cards... Solution

Details

 

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