Counting is everything

Note: This is an intermediate level problem.

Your partner (West) leads the ♠Q. Declarer wins with ♠A, plays a club to the Ace and continues with the ♥2.

1. How many spades does West have?
2. How many hearts does West have?
3. Where is the ♠K?
4. Where is the ♥A?
5. Which card will you play?

Answers

1. How many spades does West have?
   Six. South’s 1NT denies 4 cards in spade (with 4 cards he would bid 1♠). Therefore West must have at least 6 cards (with 7 cards, not vul he might have jumped to 3♠).
2. How many hearts does West have?
   Three. South’s 1NT denies 3 cards in hearts (with 3 cards he would bid 2♥). Therefore West must have at least 3 cards (probably only 3 for else declarer would not play that suit).
3. Where is the ♠K?
   With South. The lead of ♠Q denies the king.
4. Where is the ♥A?
   With West. As south showed the ♠AK, he cannot possibly have the ♥A too for his hand is limited to 6-9(10) points.
5. Which card will you play?
   The ♥Q! Protect your partner’s lone entry to his long suit. As you know your ♥Q will hold, play it now and continue with your last spade. Declarer is bound to go 2 down now as the defense will win 2 hearts and 4 spades. If you play any other heart, South will play the ♥J and continue to develop his hearts. Whatever your partner will try (play low or take the Ace) it will not help and declarer will manage to establish at least 3 heart tricks.
   

Click the Next button in the diagram to follow the play.

Things to remember:

• From a simple bid and lead you can conclude a lot! Notice that the 1NT response after a 1♣ or 1♦ opening denies 4 cards in a major suit, and that a 1NT response after the 1♥ opening denies 3 cards in hearts and 4 cards in spades.
• It’s easy to count points and distribution, if only you practice it. Here, like a puzzle, you could place your partner with ♠QJ10xxx and ♥Axx already after the first trick!
• South could have made his contract. He should have hold up the first trick and win the second spade. Then play a club to dummy and return a heart. You can jump with your Q but you have no more spades to play and whatever you continue, South will win, play another heart to his J and manage to establish his hearts.
• Most players will jump to 3NT with North’s hand. However, it would not be wrong to invite with 2NT. Even though it has 18 points, the hand is "anemic": no spots (10’s and 9’s), points are in the short suits, weak long suit and 2 little spades where South denied 4 cards. However, South will accept the invitation and bid 3NT.