From                 19th Sepember, 2007, Board 17

                                          Theme               Counting the Distribution

                                          Difficulty           * * *

                                          Dlr North          None Vul            Hands Rotated

                                                                                               for Convenience
 

Against 3♥, West leads the Club Nine.

This Problem is part of our occasional Sherlock Series, in which we show the auction and ask the solver to deduce who’s got what.  Here the challenge is to figure out the enemy distribution, and further to determine the location of all of the missing high cards.  It really is quite elementary, the clues are all there.

SOLUTION

Let’s start with the distribution:

-         For his passed hand Double, East surely has at least 4 cards in each of the unbid suits, in this case the minors.

-         West raised Diamonds to the 3-level, surely he has 4 and the missing Diamonds are 4-4.

-         West’s opening lead of the 9♣ is surely a doubleton, as East would no doubt have bid Clubs with AKxxxx in the suit.  So, the missing Clubs are 2-5.

-         Next, let’s reasonably assume that West does not have more than 4 Spades, otherwise he would have overcalled South’s 1♥ with 1♠.

The inescapable conclusion is that West’s distribution is 4-3-4-2 or 3-4-4-2.  We’ll get back to which it is later.

Now, we move on to the high cards:

-         East has the AK♣

-         West did not lead the A♦, so we can be sure that she does not have both the AK♦ (would you lead a doubleton instead of Ace from Ace-King?)

-         Thus, East has either the A♦ or the K♦ (not both, she didn’t open the bidding)

-         We don’t think that East would pass with the AK♣ and the A♦, so let’s give East the K♦ and West the A♦

-         Surely the Q♥ is with West, as East would not originally pass with a 5-4 12-count.

We’re almost there!  We’ll place the J♠ with West, making the slight stretch that East would also not originally pass a 3-1-4-5 or 4-0-4-5 11-count.

Now, it’s the final lap.  Is East 3-1-4-5 or 4-0-4-5?  We’d deduce the former, as West might well have doubled with Q9xx of Hearts.  This one is also a slight deductive stretch.

So, there we have it, Watson, this is how we visualize the whole hand:

	♠ K976 ♥ K65 ♦ T ♣ JT874
♠ AJ82 ♥ Q93 ♦ A985 ♣ 93	North    West          East            South	♠ T54 ♥ 2 ♦ K743 ♣ AK652
	♠ Q3 ♥ AJT874 ♦ QJ62 ♣ Q