Here was the original problem:
IMP scoring, East/West vulnerable, South deals.
Inference in ♥️s:
South’s 2♥️ play on the first trick strongly suggests she/he does not have the K♥️. From that assumption we can posit North’s 6♥️ opening lead as fourth best from the K♥️. Using the rule of eleven or observing that North has played two ♥️s below the 6♥️–we conclude that North started with six ♥️s and South started with three ♥️s. Bottom-line, South has no more red cards.
Inference in ♠️s:
It is unlikely that North has four ♠️s. If he/she does then those four ♠️s together with his/her remaining two ♥️s means that he/she started with no ♣️s. Which means South started with seven ♣️s. With seven ♣️s, South would be inclined to open 3♣️s at this vulnerability. Conversely, South could easily have started with five or six ♠️s.
Surefire play to make 6NT:
Cash the K♠️.
Case 1: If North shows out, then South’s remaining cards are five ♠️s and one ♣️. Finesse the ♣️ into South. If it loses, she/he will be forced to lead a ♠️–making dummy’s 10♠️ your 12th trick.
Case 2: If North plays a ♠️ when the K♠️ is led, then South has a maximum of four ♠️s left (South discarded 2♠️ earlier). Run the ♠️s and if the J♠️ does not drop then lead the last ♠️ (10♠️) to put South in with her/his J♠️. South will be forced to lead a ♣️ giving you your 12th trick.
Here was the entire deal:
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