Here’s your hand sitting East as dealer:
West North East South
3C* 3S ?
*weak, at least five clubs
EW was playing inverted minors, so the jump to three clubs showed a weak, preemptive hand with at least five clubs. So what’s your call?
You have seven clubs. You know partner has five clubs but not many points. Forget slam and forget about playing it in five clubs. You have 3N cold.
If you bid 3N, and get the contract, you can make three (nine tricks) regardless of the lead. Since you know that partner has five clubs there is only one club outstanding in opponents’ hands. If it’s the king it will drop. So with a diamond or a heart lead you will make three (seven clubs, the ace of hearts and the ace of diamonds. If you get a spade lead, you will make at least four because the lead into you makes your king of spades a winner.
Here are the four hands:
♠ J94 ♠ K6
♥ 95 ♥ A8
♦ 1054 ♦ A9
♣ KJ743 ♣ AQ109652
In the actual hand as played by East, she jumped to five clubs over 3S, going down one, not even attempting 3NT. If north bid 4C instead of 3S, East would be in a quandary because if she didn’t get a spade lead she would not make 4NT. She could take 9 tricks off the top but once the two red aces are gone she’s got no stopper in the red suits. And she’s going to get a heart lead (despite South’s good, five card diamond suit; from the bidding South knows partner has five hearts, so her best lead is from her four card heart suit) so after East takes her nine tricks, they are going to run their hearts and the spade ace for down one. Even if South leads the diamond six, the result will be the same, only the winners they take will be in diamonds, not hearts.
The only question on the hand depends on North. An aggressive north might bid 4C (Michaels Cue Bid promising 5-5 in the majors). This would be aggressive because it’s a game-forcing bid when he doesn’t have an opening hand as it doesn’t even satisfy the Rule of 20 (10 cards in two suits and 10 HCP). So to make a game forcing bid like this would be super aggressive. When this north merely overcalled 3S (a good overcall giving partner a lead), South didn’t think a nine point hand was worth taking action by bidding game, 4S. But if North bids 4C, South can comfortably bid 4H if East passes, and 4H makes.
It was an interesting hand with game for both pairs if they can find it. This hand was played 9 times, only three got it right. However, if EW is not playing inverted minors, West’s initial response would be 2C (a weak raise) and North could then overcall 3C showing the majors at a lower level so it would not force to game, and NS would find their good heart fit. Two pairs played in 3NT, making three; one pair played in 4NT, making four; two pairs played in 5C, down one; only one NS found a heart bid, playing in 3H making four; one pair played in 5S down one and one pair played in 6C, down two.