Continue by drawing trumps (finessing against East's ♥10.

You can count only 11 tricks – six hearts, a spade ruff and four minor-suit winners. The only chance for 12 tricks is a squeeze against East. For that to happen, West has to have at most two clubs and no more than three diamonds.

West is known to have nine spades, and if he is 2-2 in the minors, any play will work. If West has three diamonds, a little work is needed to take the mystery out of the deal and make sure the squeeze works when East has only four diamonds.

After pulling trumps, play dummy’s top diamonds and ruff a diamond. This clarifies what you need to play for: West beginning with 9031 shape and East with 1444.

Then continue with the last trump, throwing a third club from dummy, which now holds the singleton ♦7 and the ♣A8. South has the ♣K74. On the play of the last trump, East has no winning discard from the ♦Q and ♣QJ10. 

Best play is to draw trumps and play the ace and another diamond.    If West follows to the second diamond with the lowest missing diamond it is safe to play low from dummy because East will have to win the trick.    If East happens to have started with honor doubleton, East is endplayed.    If East has a safe diamond exit and diamonds break 3-3, the spade finesse is unnecessary.  If diamonds do not divide 3-3, the spade finesse is still available.

Also, when a second diamond is led and it is not clear who will take the trick, rise with dummy's king and play a third diamond.    If diamonds break 3-3, you have the rest; if not, the spade finesse beckons.   The key to the play is determining how the diamonds break before taking  what could be a needless spade finesse.

Win the ace and lead a spade to partner's ace so partner can lead a club through declarer's king. How do you do know partner has the ♠A?  If declarer had it, why didn't he lead a spade at trick two to get to his hand to pitch a club on the ♥A?

Elementary, my dear Watson.

Win the ♦A (too risky to duck) and play the AK of spades. If spades are 3-2 or the ♠10 has dropped singleton, play the king-ace and ruff a heart, return to the ♣Q and play all of your remaining spades. Your last three cards should be the ♥ 0, the ♦Q and the ♣7, dummy having the AK10 of clubs. 

If the player with the ♦K or the long heart started with four clubs, he will have already been squeezed. If nothing exciting appears when you draw trump, play the AK10 of clubs and hope the jack obliges. 

If someone started with the 10xxx of spades, draw trumps and hope the clubs come in for five tricks. 

Tip: 

When you have all the tricks but one, be sure to play off ALL of your trumps before cashing your remaining winners. If a squeeze exists, it is the last trump that finishes them off. In this case East is squeezed in the minors on the last spade. Play it out. 

You have can make 12 tricks whenever West holds the ♠A, which on the bidding is fairly certain. After winning the diamond lead with the ace, you just draw the trumps, discarding diamonds from the table. The only way to make 12 tricks is to utilize dummy's spade suit, despite the fact that there appears to be only one (club) entry to the dummy. One possibility is to seek a second club entry to dummy by leading the two of clubs, intending to finesse dummy's 10. This would rely on luck, since you would need West to hold the ♣J. In any case, an alert West would always spoil your plan by inserting the J if he held it.

In fact there is no need to rely on such a dubious approach. You should lead the queen of clubs and overtake it with dummy's king. You then play the ♠K, discarding a diamond. West wins with the ♠A and has no good return. A spade will give the lead to dummy, allowing you to throw a diamond and club. Similarly, a club exit will promote the 10-9 of clubs into an entry, no matter who holds the ♣J.

As you have no side-suit losers, you need concern yourself only with the situation in the trump suit. In such circumstances there is really no excuse for failing to work out the safety play required. On this deal, you can easily make the slam if trumps break 2-2 or 3-1, so you must make up your mind what can be done against a 4-0 break.

The bad news is that if East holds all four trumps it's time to concede down one and move on to the next deal. When West holds four trumps you can pick them up for one loser, but only if you play the jack on the first round of trumps! In this case, West wins with the ace and you can later run the 8 and then the 7 through West, avoiding the loss of a further trick to the 10 or 9 of trumps.

The same sort of play would have been required if all the pips were moved up one and you held like A-K-5-3 opposite Q-9-8-7-4. You can only pick up ♠J1062 on one side, so you should begin by playing the queen.

The crux of the deal is avoiding a second diamond loser. In isolation, the best play in diamonds is to finesse the 9 on the first round. This succeeds immediately when East holds the ♦J10 because the 9 will force West's king. When the 9 loses to the jack or 10 from West, you finesse the queen next time. This gives you two chances, but that line fails on this layout:

The way to overcome this arrangement is to eliminate the clubs and hearts before touching diamonds. The only trap is failing to manage the entries required to bring this about.

You must ruff three hearts to eliminate the suit and then return to dummy to lead diamonds, so you need four entries in all. After taking the opening lead with the ♥A, you immediately ruff a heart high and lead another high trump to dummy's ace. A third heart ruffed high eliminates the suit, as planned, and you will still have the ♠4 left. Use it to cross to dummy with the 8 to ruff dummy's last heart, thereby eliminating the suit.

The ♣K and a club to the ace removes the clubs and returns you to dummy for a fourth time.

Now it is time to play a diamond and cover East's card. East will likely play the ♦8, West takes the ♦9 with the jack but is endplayed for his troubles. He has the choice of giving you your 12th trick by returning a diamond into your tenace or playing a club, which gives you a ruff-and-discard. In that case you throw a diamond from dummy and ruff in your hand. After cashing the ♦A at trick 12 you make the last trick with dummy's remaining trump.

The result is the same if East plays the ♦10 on the first round of the suit. West takes the queen with the king, but your ♦A9 is now a tenace and you will still be able to hold your diamond losers to one if West returns a diamond.

You should thank West for not leading a trump. It destroys the entries necessary to bring off the above elimination and endplay on the given layout.

If the diamonds break there is no problem, but if they are 4-1 you have only 9 tricks.  You could try the ♥Q at trick 3 but is that a sensible play?  West is very unlikely to have switched to the ♥J when holding the King, and the ♥Q might be useful later as follows.  

Win the ♥A, draw trumps (which break 2-2) and test the diamonds.  If they break 4-1 you can ruff your last club and exit with the ♥Q.  If the ♥K is in the same hand as the singleton diamond, that player will then have to give you a ruff and discard for your tenth trick.

Partner could have 2 tricks in the black suits in which case the contract is always down, but in reality that is very unlikely.  A more likely way to beat the contract is to win 2 diamond tricks and a black King from partner.  The best defense is to continue with a low diamond at trick 2.  Look at all four hands and you will see that although this switch is by no means certain to succeed, it represents your best chance. 

This hand is all about the heart suit.  Do you play for the drop or finesse the ♥J?

East clearly has long spades so is maybe short in hearts.  However, you should try to get a count of the hand.  Your first move should be to ruff the club with ♦10 as this preserves your low diamonds to use to get to dummy.  When you cash the ♦A, the ♦J falls from East.  Then you can play the ♦8 to the 9 in dummy, ruff a club, and then re-enter dummy with the ♦6 to ruff the last club, on which East discards a spade.  You now know East started with 3 clubs and 1 diamond.  West's initial lead of the ♠7 would generally show a 4 card suit.  If he held a five card suit he would have lead his lowest card, and with only 3 spades, we would have heard more from East (holding 8 spades).  Hence you can be confident that East's shape is 7213 and that the Q♥ will drop doubleton. 

This is a hand which really plays itself.  If West has the expected ♠A, then you also hope that he is controlling the club suit.  Simply play out most of your trumps.  If you view the full hand you will see that in the end position, West will hold  ♠AJT and ♣QJ8 and have no good discard.  A spade is fatal as declarer now plays a spade towards dummy ensuring 2 tricks with the ♣A as an entry.  If West throws a club in the end position then he is stuck when a spade is led.  He has to duck to avoid giving 2 tricks in the suit as before, and now having avoided a spade loser, declarer simply plays 2 rounds of clubs, establishing a second club winner for himself.

It is often a good thing to play out a long suit even when you cannot foresee the exact ending as defenders often will discard incorrectly, or as in this case, the play to the final few tricks just falls into place.

With the ♥ K marked with East, South does best to play low from dummy and win the ace intending to use the ♥Q as a later throw-in card. South draws trumps, strips diamonds and exits a heart to the queen and king. East is fixed. A heart return is a ruff and discard while a club return goes into “Jaws” (the AQJ). Either way it's all over but the shouting. An equally divided side suit such as hearts in this example can often be used as a throw-in suit to force a favorable return. However, the side suits must be stripped, the opponents' trump drawn, and at least one trump must remain in each hand before the 'grand exit' in the evenly divided suit. 

You know declarer has 6 cards in the majors and hence 7 in the minors.  His ♦K cannot be singleton as he would have played it earlier whilst he had trump entries to dummy so you should take the ♦A when the King is led.  Now count delarer's tricks.  4 spades, 1 heart and 4 diamonds only comes to 9.  If South has ♣KQ you can do nothing, but you must avoid giving declarer an free club trick with the King.  Just exit with a diamond and sit back to collect 2 club tricks when the layout is as shown.

The obvious line is to finesse in clubs, but if East should hold all 4 missing clubs, you will need to lead the suit 3 times from dummy.  The only dummy entries are in hearts, so you may need to create 3 entries in that suit.  One thought is to play a heart to the queen, finesse the club (West showing out) and then another heart towards dummy, intending to finesse the ten.  The problem with this line is that a thoughtful West could scupper you by inserting the ♥J on the second round, blocking you out of your third entry.  What about leading low to the ten on the first round?  It wouldn't matter if West played the Jack as you could still win 3 tricks in hearts by overtaking the King with the Ace later.  Well, that's OK as far as it goes but you would look very silly taking a possible losing heart finesse to later find that the clubs were not 4-0 and all you needed was two club leads from dummy! 

The solution is simple: at trick 2 play the ♥K to the Ace on the table and then finesse a club.  If West follows then use the ♥Q as a second entry to finesse clubs once more giving you 5 clubs, 2 hearts, a spade and a diamond.  When the clubs prove to be 4-0 then you can now finesse the ♥T for the extra entry.  Obviously if the heart finesse loses you will be defeated but at least you will have played the hand as well as possible.

At the table, the declarer found an excellent line.  Win the ♣A and duck a spade to West.  Win any return and lay down the ♠A, leaving one trump outstanding.  Then you can play diamonds, discarding 2 clubs from dummy, and cross-ruff the hand.  West could score the top trump whenever he liked but declarer had 10 tricks.  So can the contract be defeated?

Consider the effect of East playing the ♠Q on the first round of trumps.  If declarer ducks, East is in to cash 2 club tricks to easily beat the hand.  Hence declarer must win the ♠A.  Now he is doomed to defeat as he cannot play on diamonds without drawing another round of trumps but this allows West to cash another trump, destroying the cross-ruff potential.

Could the spade play be found at the table?  Well, East can visualise declarer's hand at trick 1.  Since partner would not lead the 2 from three small, the lead must be a singleton, and the bidding marks South with a void heart.  Hence declarer must have the hand he actually holds as an absolute minimum.  If declarer has better spades then there will be no chance of beating the contract.  On this reasoning, the ♠Q at trick 2 can hardly cost.  That said, I expect there are not many who would not find this imaginative play.