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Can you beat Zia? (logic problem)

A good friend wins a lottery prize of "An evening with Zia" and invites you along for the evening. He commissioned someone to create special hands for the occasion so you have had a session of difficult to bid slams, interesting defensive problems and a smattering of end-plays and squeezes. On the last hand of the evening your friend, Mike, graciously allows you to partner Zia!

Mike is dealer and opens 1NT (12-14) which is passed out. Zia leads 3 and dummy is revealed:

North
K53
J932
J72
K74
East
QJ42
A8
10854
Q96

The 7 is played from dummy, you play the 10 and declarer wins with the K.

Mike leads K and then puts the rest of his cards face down on the table and says he has had enough; his favourite cards are the black jacks and he hasn't had one all evening!

Mike then sets you and Zia a challenge; can you work out how many points he has? You each take turns to make a guess or pass; the winner is the first to guess correctly. However, make a wrong guess and you lose immediately! Zia goes first.

Mike then passes you a note which reads "Good luck, you should be able to beat Zia".

Bonus question: Why did Mike pass you a note?

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