From                   28th March, 2007, Board 12

                                          Theme                Counting the Distribution

                                          Difficulty            * * *

                                          Dlr West            N-S Vul

As West you hold:

   ♠ K5

   ♥ 94

   ♦ AK954

   ♣ 7432

West    North   East     South

Pass    Pass    1♥        Dbl

Rdbl    2♣       Pass    Pass

Dbl      Pass    Pass    Pass

Here’s a Problem with a difference.  You are in the West seat, the auction is over, what are the distributions in all 4 hands?  It’s a revealing auction, what can you deduce?

Let’s treat it as a miniature Sudoku puzzle.  Here a matrix of what we know:

                                    You      North   Pard     South

            Spades               2

            Hearts               2                       5

            Diamonds          5

            Clubs                 4                       2

We have assumed here that Partner would not be defending 2♣ doubled when he has a 6-card Heart suit.  Nor would he defend 2♣ doubled when he has just one Club, our Double of 2♣ was a cooperative effort after all.  And, it hardly seems likely that the opponents have stumbled into a 6-card fit when they had two other suits from which to choose, so surely Partner has exactly 2 Clubs.

Now let’s look at the Spade suit.  North has 3 or less (otherwise she would have bid 1♠ over the Redouble), Partner has 4 or less (otherwise he would have opened 1♠), and South has 3 or 4 (with 5 she would overcall 1♠, with less than 3 she would not double 1♥).  The inescapable conclusion of this is that the Spades are as shown in our updated diagram:

                                     You      North   Pard     South

            Spades                2          3          4           4

            Hearts                2                      5

            Diamonds           5                      2

            Clubs                  4                      2

Next, let’s look at the North hand.  We know about the 3 Spades, of course, and we also know that she has show a clear preference for Clubs … let’s not forget that she could have passed the Redouble and let her Partner pick the trump suit.  What is consistent with North’s bidding?

            3-3-3-4?          No, this hand has no clear preference for anything, with this shape she would pass and let South choose.  No reason to go to a potential 4-3 two-level contract in Clubs when a 4-3 Spade contract at the one-level is likely available.

            3-5-1-4?          Yes, this is possible from the North point of view, she can hardly pass and risk a 2♦ bid from South.  But that would give South 4-1-5-3, and we doubt that she would have stood for 2♣ doubled when she had a 5-card Diamond suit that she could run to.

            3-4-2-4?          That’s it!  As before, North could not risk a Pass, that might fetch a 2♦ bid from South.  Is North’s 3-4-2-4 consistent with South’s actions?  Yes, that would give South 4-2-4-3.

So, the completed matrix is:

                                     You      North   Pard     South

            Spades                2          3          4           4

            Hearts                2          4          5           2

            Diamonds           5          2          2           4

            Clubs                  4          4          2           3

And the complete deal is: