Solution doubledummy Problem 5

W leads the spade A.
Next, if W plays Club or dia, then N-S get four dia, and 5 club tricks by cross-ruffing, the first ruffing should be done in South, which is possible whether dia or club is led.

Thus, W has to play heart. N plays the next bigger heart, and E wins.
Next if E plays club or dia, then the same solution as above.
If E plays hearts, then 1 spade, 1 heart, 3 dia and 4 club tricks via cross-ruffing.
So, E has to play a spade. S plays Queen of spades.

Now, 4 club, 3 dia, and one spade tricks are easy to see. Where do we get the 9th trick from?

We consider 3 cases, depending on what W discards on the second spade trick:

CASE 1: W discards a club!

In this case, N-S cash the Ace of clubs and dias, and ruff two each to end in North.
The situation is as follows:

North has: Club 9 5, Heart Q 6
East has: Spade J, Heart K 5, Dia 10
S has: Spade 7, Heart 3, Dia J 9
W has: Heart J 9 8, Dia K

N-S need two more tricks.
North, then plays a club. East has to play the spade, or else N-S get their required 2 tricks. South then discards the heart. W has to discard the heart, or else S wins the remaining three tricks.

The situation now is

North has: Club 9, Heart Q 6
East has: Heart K 5, Dia 10
S has: Spade 7,  Dia J 9
W has: Heart J 9, Dia K

 There are three possibilities now, and in either case, it is easy to see that N-S get two more tricks.


CASE 2: W discards a dia!



In this case, N-S cash the Ace of clubs and dias, and ruff two each to end in South.


The situation is as follows:


North has: Club 9 5, Heart Q 6
East has: Spade J, Heart K 5, Dia 10
S has: Spade 7, Heart 3, Dia J 9
W has: Heart J 9 8, Club K

S gets the dia J, and then plays the dia 9, thus getting two more tricks.


CASE 3: W discards a heart!

Lead a heart from South, and a small heart from North.

If E plays the king, then N-S have two additional heat tricks, (and maybe one less spade trick, if E leads the spade next).

If E does not play the king, then W wins the trick.

Then, whatever W plays, go up North via clubs, and play heart from North, and ruff it in south, to create an additional heart trick.


Fantastic problem!!!!

Solution doubledummy Problem 2

Play the jack of spade from North, then no matter whether east plays the ace or not, you have 4 club, 3 spade, 3 dia, and one heart trick.

Lots of cases, though I don't see why this is DR7.

Solution doubledummy problem 6

http://doubledummy.net/Problem0006.html

Pick 3 heart tricks down south discarding S A K Q from north.
Then pick 2 dia tricks in north and then play the spade 2.

CASE 1: east plays a small spade.
Then take the spade in south.
Now the hands look like:
South: heart J 8, dia Q 10, club 3 2, spade 3
North: C A K 8 7 6 5 4

case 1 a): west has at most three clubs.
In this case give a club trick to west, then west either gives a trick to south in dia/hearts, or west gives a club trick to north, in either case north wins the remaining club tricks.

case 1 b): west has more than 4 clubs,
this means east has either only one heart, or only one dia.. in either case south wins two dia/heart tricks, south keeps winning until west is left with 3 clubs, at which point south gives one club trick to west and north wins the rest.

CASE 2: east plays the jack of spades.
in this case get one spade trick, one heart trick and one dia trick

Now the hands look like:
South: heart 8, dia 10, club 3 2
North: C A K 8 7
then we win just as in case 1.

Solution doubledummy problem 4

http://doubledummy.net/Problem0004.html


Take the heart trick down south with A
Then play a dia and take the trick up north with the king.
Then lead a small club!

CASE 1: east plays 4 of C
Take two club tricks in south
then go north by king of heart, ruff heart in south
pick ace of spade and then go north using king of spade and then ruff spade in south.
then give a club trick to east.
at this point, east leads either heart or spade
North has D A 10, C 9
South has D J 9 5
West has D Q 8 7
so, on the H/S lead from east, play dia J from south. Now, if west plays queen then get it with the ace and then get the remaining two tricks. Otherwise, drop club from north and the remaining are winners.

CASE 2: east plays J or K of clubs
Then get the trick down south using Queen, or Ace depending on whether east plays J or K.
then play dia small, and get it with the ace, then play dia 10 from north and J from south, and play dia until west takes it with the queen.

CASE 2a): west leads dia, club or spade next.
pick spade ace, club queen and all the remaining dias.
now, look at the situation when south plays the last dia to decide the card to be discarded in north!
North, at this point has spades K 9, heart K 3
South, at this point has spade 2, H 9, D 2, 6


now, if east has only one heart, then we win 2 heart tricks, 1 spade trick, and 1 dia trick! similarly if east has only one spade!
thus, east has the following hand S QJ  H  Q.

now, if on the lead of 2 of dia from south, east discards a heart, then north discards a spade and wins 2 heart tricks, 1 spade trick and 1 dia trick! similarly for the case when east discards a spade.


CASE 2b): west leads heart!
north takes it with the king and comes south using spades A, and then takes the remaining dia tricks.

now, look at the situation when south plays the last dia to decide the card to be discarded in north!
North, at this point has spades K 9, heart  3, C 2
South, at this point has spade 2,  D 2, C Q 6

now, when south plays dia 2, east has to have two spades and one club, else we win just as in case 2 a).  Thus, north discards heart 9.

so, now the hands look like,

North, has spades K, heart  3, C 2
South, at this point has spade 2,   C Q 6

East has Spade QJ, C 10

south plays spade, after which the three hands look like,


North, has heart  3, C 2
South, has spade   C Q 6

East has Spade Q, C 10

now, if west does not have a heart, then we win one heart and one club trick, else two club tricks.



!!!! Really, DR 7!!!!

Solution doubledummy problem 3

http://doubledummy.net/Problem0003.html
  take the K spade from south lead a dia from southCASE 1: west does not play the king In this case north plays small and south wins this trickThen north takes the ace of dia in the next trick, then takes two spade tricks and gives a spade trick to east.the east, at this point has only hearts, so, the east is forced to give one heart trick to north, then north gets two more spade tricks and two club tricks in south to complete the required 10!
CASE 2: west plays the king on the dia leadthen, take the trick with the ace from north

  then pick the two spade tricks from north and give a spade trick to east

  discard all your diamonds from south on these spade trickseast's hand is H AQ98765, D 8

  South is C AKJ98765

 North is S 32, H KJ10, D 32, C 2

  we come to west's hand in a little while CASE 2 a): east takes the diamond trick and then the ace of heart and then leads heart

  in this case north takes two heart tricks, two spade tricks, and gives south two club tricks to finish with the required 10

 CASE 2 b): east takes the diamond trick and then gives a heart to northnow, North takes two spade tricks

 at this point north has two hearts, a diamond and a club

  south has 4 clubs

  now, consider west's hand

 if west has at most 2 clubs, then north leads a club and takes all 4 tricks down south (we need only 3)

  if west has no diamond, then north takes a diamond trick and then gives the lead to south to cash the two club tricks

 so, west must have at least 1 diamond and at least 3 club, which means all hearts have been discarded

  this is good news because now, west cannot lead the hand back to east's heart ace

  in this case north gives a diamond to west

 and then west is forced to give 3 club tricks to south

CASE 2 c): east gives a heart trick to north

11:12 PM north in this case returns the diamond trick to south, and then we are back to either case 1, or case 2

  CASE 2 d): east takes the ace of heart and then gives a heart trick

  in this case north picks two heart tricks

11:13 PM then two spade tricks

  and two club tricks

  to finish with the required 10

Solution doubledummy problem 1

 http://doubledummy.net/Problem0001.html  take the heart in souththen take a spade with the ace discarding heart in north case 1: when east gives a small spadein this case take the club AKQ and heart A

 and then come south using clubsand then take the spade king and then give a spadewest only has diamondsnow, it is easy, get two club tricks and one diamond trick in north, and one diamond trick in south!! case 2: east gives a big spade!go north using clubs and pick the 6 club tricks and one ace of heart (by discarding a club of south on the ace of hearts)at this point north ka hand ye haiH 54D Q3now if east has discarded all hearts, then it is easyso, east has at least one heart 2 a) east has at most 2 dias, 1 heart, at least 1S2 b) east has 3 dia, 1 h, no spades in 2 a) south has Spade K , dia A 8 2in 2 b), south has spade K 5, dia A 8this is because the last discard, spade 5 or diamond 2 can be decided by south based on east's discard! so, in 2 a), north leads the queen of diamond, wins 2 dia tricks and one spade trick! in 2 b),   if west has only one diamond, then get one two diamond and one spade trick!if west has at least three diamonds, then get two spade and one diamond trickif west has two diamonds (and two spades) then north leads a small dia and takes it in south with the ace. Then, if west has the K dia, then give a diamond to west's king and then get two spade tricks in south, else get the K spade in south and Q dia in north.