One line would be to take a spade finesse, just losing a club if the finesse succeeds. Another line of play is suggested by the lead and indeed will only fail if West has all 3 top diamonds. Ruff the opening lead and draw trumps finishing in dummy. Lead the ♦J, throwing a club if East declines to cover. Win West's return and lead another high diamond, discarding your spade loser unless the diamond is covered. A double ruffing finesse and loser-on-loser play. 

There is no problem if trumps come in, and if not you have the spade finesse to fall back on. If you play correctly, however, you can also get home on certain other layouts. The key play at trick one is to duck in dummy (preserving the ace) and ruff in hand. Now play off two top trumps. Lets say East turns up with Qxx. Now ♥ AKx ruffing followed by a trump exit. If hearts started 4-3, the defence are doomed. A spade concedes the contract and a fourth heart sets up dummy's long heart with a spade entry to get there. If East leads a club, then you can win the ace and now ruff a further heart to establish the long card.

The opening bid tells you that the King of hearts lies over the Queen, so let the first trick ride round to your Ace. Now take two top trumps and play AK and a diamond ruffing. Now cash the AK of clubs and lead the ♣J. If East follows small discard a heart and West must concede a ruff and discard. You make this contract whenever West holds the ♣Q and also when the Queen falls doubleton offside.

The slam is very good, even on a heart lead. You can cash 2 rounds of trumps (no problem if the Queen falls. If not, you start on the clubs and provided the hand with the last trump holds 2 clubs, you are able to discard your losing hearts. If you look at the full layout, you will see that this line is unsuccessful, as West ruffs the second club and cashes a heart trick. Now imagine you are in 7♠. Now you have to take the spade finesse and draw all the trumps before starting clubs. The marked ruffing club finesse see you home. Hands where making a grand slam when the small slam will fail are rare, but they do happen from time to time.

You have 12 top tricks and the best plan for a 13th is by playing to set up a long heart. As the only way to reach any established long card in hearts is with a trump, you will need the trumps to break no worse than 3-1. How will you go about setting up the hearts, though? If West has a doubleton heart, you need to be careful.

After winning the club lead with dummy's ace, you should cash the ♦K and ♦Q, followed by the ♥A. You then cross to dummy with a trump and play the ♦A, throwing the ♥6 from hand. Now you can afford to ruff a heart in your hand with a low trump. You return to dummy with a second round of trumps and lead another low heart, ruffing it with the ace to circumvent any potential overruff. Next you play another trump to dummy, drawing West's remaining trump in the process. All that remains to do is to you cash the ♥K  and ♥10, discarding your losing clubs and leaving you with a trump to take care of dummy's ♣J. You make six trumps, three hearts, three diamonds and a club.

If you do not discard a heart on the diamond ace, you will end up promoting a trump trick for West. In fact, the recommended line has close to an 11% advantage over playing on hearts without discarding a heart on the ♦A.

You see nine sure tricks and the potential for three more in spades if East has the king of spades and at most three spades.  West's three heart preempt seems somewhat light without both the king of hearts and the king of spades, but could be made without the king of spades. If West has the ♠K, it might be singleton or West might be endplayed if he wins a trick with the king of spades.

Think about West's distribution. Assume West started with seven hearts for his preempt. 

It is essential to determine West's holding in the minors. If West has four or more minor suit cards and the king of spades, the play of the ace of spades will either capture a singleton king of spades or will allow you to endplay West by leading another spade. Play the AKJ of diamonds first. West discards a heart on the third round of diamonds. Next play the ace and king of clubs. West discards a heart on the second round of clubs. So West started with three spades assuming he started with seven hearts for his preempt.  Now you need to assume East started with the king of spades. You know East started with three spades. 

You play your ten of diamonds and overtake with dummy's queen. You then play queen of spades and both opponents play low. The play of the jack of spades has the same result. Both opponents play low. Stop! If you continue playing spades, you will capture East's king and end up in your hand with no entry back to dummy to exploit your spade winners. You play the last diamond in dummy and discard your ace of hearts! Then lead dummy's ten of spades to your ace of spades and capture East's king of spades. 

Now lead your heart. West plays his king and you play dummy's six. Since West has only hearts remaining in his hand, he must lead a heart to dummy's queen giving you access to the last spade winner.

You won't be able to ruff spades in the dummy so your best hope is to set up the diamond suit. Win the lead and draw trumps. Now play a diamond and finesse the Knave when West follows low. You expect it to lose but now establishing the diamonds is easy and you use the ♠K as an entry for them. If you play off the diamonds from the top, you will fail when the suit breaks 4-1 through lack of entries.  

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. 

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 need a trump coup to pick up West's trumps, which means ruffing twice in dummy and ending in your hand at trick 11 with dummy holding the ♠AT. East will hold the ♥A as otherwise West would surely have cashed that card at trick 1. Hence cash the ♦A, ruff a diamond and lead a heart. If East ducks, he loses the ♥A as you can discard a heart on the ♦K and just lose a spade trick. Say that East goes up with the ♥A and returns a heart (as good as anything else). Win the ♥K, ruff a diamond, and get back to your hand with a club. (To make this, you must find West with at least two clubs.) Dummy remains with the ♠AT and the ♣KQ. You remain with the ♥Q, the ♦K and the ♣Ax. Play your red-suit winners, discarding clubs, and wind up with the last two tricks. If West ruffs a red winner, overruff, cash the ♠A and take the last two tricks with clubs.

You can count eight winners and another four if spades prove to be 3-3. You need to consider what might be done if the spades are not 3-3. You have an extra chance if West holds the ace-doubleton in spades. After drawing two rounds of trumps with the king and queen, lead the ♠2 from hand. If West rises with the ace, you have four spade tricks, so West follows small and dummy’s king wins the trick. Now a low spade is played from dummy to your jack and West’s ace.

This leaves West on lead with only clubs and hearts. If he exits with a club, you ruff in dummy and throw a heart from hand. After cashing the ♠Q, you throw a second heart from hand, ruff a spade to establish a spade trick in dummy. Then cross back to dummy with a diamond and discard your ♥ J on dummy’s spade winner.  A heart exit from West at the critical point gives you an even easier ride.

You can pretty much guarantee that the lead is a singleton, so you must rise with the ♦A. Now you have good chances. Draw trumps and play a low diamond from the table. East must duck this trick to give you a problem, but now you cash the ♣A and 3 hearts finishing on the table. Then play the ♣Q and throw a diamond away. West must win and only has clubs left, so has to concede a ruff and discard, allowing your other diamond loser to disappear.

You can always make 12 tricks provided East has no more than two clubs. After winning the ♣A, you should cash the ace of trumps and lead a low trump to dummy's 10. Next you ruff a club back to hand and play two more rounds of trumps. When East did begin with one or two clubs, such as on this full deal:

When you play the last trump, throwing a club from table, East is in trouble. You know he began with seven diamonds a trump and, hopefully two clubs. If East reduces to three diamonds, you will play the A, K and another diamond. East wins the trick and has to return a spade, allowing you to take the last three tricks with the top spades and the ♦9. Whenever East keeps four diamonds, and so only two spades, you will counter by cashing the two high spades, reducing East to ♦QJ87. This allows you to make three of the last four tricks by leading the ♦2 to dummy's 10. When East takes the 10 with the jack or queen, he will be forced to lead a diamond, allowing your 9 diamonds to take a trick. Two more high diamonds will get your trick total to 12.

You should see that it was vital to ruff a club on the above layout, for otherwise East would defeat you by coming down to two spades, three diamonds and a club on the last trump. After winning his diamond, he would be able to play a club to his partner.

With West holding long spades, ruffing spades in dummy is not an option.  Those diamonds look good and should provide the tricks you need.  Win ♥A, draw trumps (West holding 2 and East 3) and start on the diamonds by playing towards dummy.  When West plays small you play....?

The correct play is to finesses the ♦J.  No matter that this loses.  You can win the spade return with your Ace and then play diamonds, ruffing the fourth round if nescessary and then use the ♠K as an entry to the established diamonds.

If you had originally played diamonds from the top, you would be defeated when East holds ♦QTxx, as you would then lack the entries to establish and cash the suit. 

Before playing to the first trick, you need to form a plan. You can count nine top tricks and you can add at least two more in clubs as long as the suit breaks reasonably favourably. Also, if trumps are no worse than 3-1, you  can use two diamond ruffs as entries to set up the clubs. All of this makes it imperative to win the first trick in dummy, so play dummy’s J♥ . Once East follows with the 6♥, you can put your plan into action.

At trick two, cash the A♣  and ruff a club low in hand. After ruffing a diamond with dummy’s 4♥ , cash the K♥  and ruff a club with the 10♥ . Next ruff a diamond with dummy’s Q♥ .

All that remains is to cross back to hand via a low spade to the ace to draw West’s last trump with the ace, discarding dummy’s remaining low spade. A spade to dummy’s king is followed by the K♣ , leaving dummy with the two established clubs to cash. 

The slam is no worse than the diamond finesse, and you may be able to duck a diamond to West in the endgame to ensure a diamond return to your AQ.  If your diamonds were as good as AQ9 you would have a certain endplay, but that is not the case here.  Still, you win the club lead and cash the ♠ K finding a 2-1 break. Now a club ruff, then ♥AK and a heart ruff high is followed by a trump to dummy.  Your plan is to ruff another heart and then  use dummy's last trump as an entry for the diamond finesse.  However, when you play the fourth round of hearts from the table, East shows out. Now all you need to do is discard a diamond.  West will win this trick but then must play a diamond into your AQ or concede a ruff and discard.

Your plan must be to avoid losing 2 spade tricks, and hopefully, clubs may provide a parking place for a spade loser. If West holds ♣QJ you have 3 club tricks, and ♣Q9 or ♣J9 allows you to take a ruffing club finesse to get a third trick in the suit. When you cash the ♣AK, however, nothing special happens. Now you must play for an elimination. Cash the ♥A and ruff a club before playing the ♠J from hand. You hope that East holds ♠Tx, which is twice as likely as KT or QT. Assume West covers the spade. You win the Ace, ruff the last club and play a spade towards the ♠9. If West rises with an honour, he establishes the ♠9 when the ten falls. If West allows East to win the trick, he has to concede a ruff and discard.

Declarer noted that the heart suit had promise, so he proceeded to show that he would make 12 tricks if he could extract all of West's minor-suit cards.

Declarer took the diamond lead in hand with the queen and cashed the ♦J. Next he played the ♣A, ♣K and a club to dummy's queen, pleased to see that the suit was 3-3. When both defenders followed to the ♦K, declarer permitted himself a small smile as he continued with the ♦A throwing a second low heart from hand.

Now declarer led a low heart from table with the intention of covering East's card. When East put up the ♥10, declarer played the queen. West won the trick with his king, but he had only major-suit cards remaining - and no winning option. If he chose a spade, declarer would make three spade tricks. When West exited with the ♥6, hoping his partner had the 9, declarer produced that card and claimed the slam. 

After getting the news about the unavoidable trump loser, declarer paused to consider what he needed to make the slam. Obviously, he needed to play four rounds of diamonds with East following suit so that he could discard two of his club losers. If this came to pass, the fifth diamond would provide a place for his last club, restricting the defenders to East's trump trick.

Declarer realized that if East started with four diamonds, he would be twice as likely as West to have the ♦J, so South finessed the ♦9 at trick four. After it held, declarer cashed ♦A, crossed to dummy with the ♥K and played the ♦K and ♦Q, discarding clubs from his hand as East helplessly followed suit. When East ruffed the next diamond, it was a trick too late as declarer discarded his last club. This was the only trick declarer lost.

Note that if it had been West rather than East who had the trump trick, declarer would have started diamonds by cashing the ace and then finessing dummy's 10 on the same logic that led him to the winning line on the actual layout: To make the slam, declarer needed for the opponent with the trump trick to follow to four rounds of diamonds.

Any discard from dummy on the third heart is worthless, so it may appear that the slam depends upon finding West with the K♣. Declarer had a better idea, setting out to play the deal along elimination lines. He ruffed a spade at trick two, led the J♦ to the queen, and ruffed a second spade with the A♦. A trump to the 7 permitted a third spade ruff, eliminating that suit. Next he cashed the A♥ and ruffed the Q♥, removing that major from the North-South hands.

West had shown up with 2-1 in the red suits, so he was credited with an original 6=2=1=4 distribution, making the contract 100%! Declarer played clubs in the normal way - ace and a club to the 10 and queen. After East won the K♣, there was a pause because East had started with only two clubs and was forced to give a ruff-and-discard. Declarer's club loser was thrown and the ruff taken in dummy, so 12 tricks were made.

If West had turned up with four or more cards in the red suits, Declarer would have led a low club towards dummy's queen without cashing the A♣ first. With West holding the A♠ and probably the QJ♠ as well, he would be unlikely to have the K♣, too. Declarer's idea was to cover West's card, hoping East began with K J x (x), K 10 x (x) or K J 10 (x).

Even if West would never play the K♣ when holding it, this plan offers better than a 50% chance of making the contract. When East wins his club trick from such a holding he is endplayed, forced to concede a ruff-and-discard or lead away from the K (or the 10 or J when West plays the J or 10 on the first round of clubs).

Win the club lead and draw trumps.  Run off your clubs and discard a diamond from dummy.  You could take the heart finesse now but you have a better plan.  Go to dummy with a spade and lead a diamond from dummy.  If East has the ace you can discard dummy's heart on the king of diamonds and if West has the ace of diamonds you can fall back on the heart finesse.

Essentially, you get to try two finesse for the price of one.  You go down only if both finesses are offside and that is just 25% of the time.

For the record, what are the chances of the heart finesse working?

50%
A little less
A little more
Other

This is a serious question.  Think about it a moment.

If you think about the bidding you will recall that East did not double North's 4H cue bid.  On auctions like this one, East might well double 4H to suggest a lead to West.  If East has a hand such that he does not welcome any other lead, he might elect to double to help West with the opening lead if West is not sure what to do.

I estimate that the heart finesse will work at least 60% of the time.

It seems natural to test diamonds by cashing the Queen and continuing with a diamond to the Ace, but playing this way diminishes your chance of success. Clearly there will be no problem if the trumps break, but if either defender has 4 trumps, you will need to score your small trumps separately, and that means planning to reduce your trump length from the beginning.  The ♦Q is needed as an entry so you should start with a diamond to the Ace.  Cash the ♥A and return to the ♦Q.  If both opponents follow,, come back to hand with a heart ruff, draw trumps and claim.  If the trumps are 4-1 you are in the correct hand to do something about it.  Look at all four hands to see one of the distributions we are guarding against.  Ruff a heart, play 3 rounds of clubs, discarding a spade from hand, ruff another heart, and return to dummy with the ♠K.  Now your trumps have been reduced to the same length as East's, and the lead of either a heart or the club from table gains you a twelfth trick.  If East doesn't ruff, you score your small trump.  If East does ruff, you discard your spade loser and then sit with K7 of trumps against East's J.

Obviously, success is not guaranteed in this contract.  You need a favourable distribution in the side suits.  However, the key point is to see the possible need for a trump reduction play and retain your entries appropriately.

This is a hand which screams for the use of elimination and throw-in technique.

At trick 2, ruff a diamond high, return to dummy with a trump, and ruff another diamond high.  Return to dummy with a trump and lead a spade.  Finesse the 7 if you can and West is endplayed.  If East plays the 8 ,9 or 10, win with the Ace, return to dummy with a trump and lead another spade.  Again finesse the ♠7 if possible but if East plays an intermediate card this time you can afford the Jack as you will then sit with a major tenace in spades (K7) 

Sound technique is to ruff the second spade high, cross to hand with a trump and ruff the remaining spade high - on this trick East plays the ♠Q.  Now draw the remaining trumps (they break 2-2). Then cash ♥AK and ruff a heart - both follow but the Queen does not drop.  By this time you can place West with ♠AKJxxx and probably only 3 hearts as else he would have a 64 shape in the majors and 10 points and would most likely have opened 1 spade rather than 2.  So now you can cash the remaining trumps, discarding the ♣J from dummy. At this point, West will have a spade and 2 clubs, whilst East will have a heart and 2 clubs.  All you have to do is play off the 2 top clubs and claim.

The ♠A might be onside, or the club suit might break.  You might think that there could also be a squeeze if West holds the ♠A and 4 clubs, but for the squeeze to operate, you would first need to lose a trick, else West will always have a spare discard, and you cannot give up a trick without the defense cahing a second winner - so that line's no good.

You do have one additional chance - the ♦QJ might fall in 3 rounds, thus setting up the ♦10.

The correct line is draw trumps, cash ♦AK, cross to dummy with a club and ruff a diamond.  If the ♦QJ have fallen, that's 12 tricks, if not then test the clubs before finally playing a spade towrds your King.

If you discard one of your low diamonds on the ♥A, you will go down, as you can see by examining the full deal:

To make the grand slam, you must discard the ♣10 on the ♥A. Now when you play on clubs and find that the suit splits 4-0 with all of them on your left, you can cash the top clubs, enter dummy with a trump, ruff the last club good, get back to dummy with another trump and - finally - discard your losing diamond. Well played!

As you can see, a club lead would have defeated the contract, but West would always lead a diamond after his partner doubled 2♦ . Would a double of 7♠  by East have canceled the earlier double (indicating high cards in diamonds) and asked for a different lead?

A situation eerily like this came up in the 2009 Bermuda Bowl in Sao Paulo, Brazil, where at both tables a bid was doubled for a lead and the final contract, a slam, was doubled again. At both tables, the doubler simply wanted to increase the penalty that was coming from the opening lead he thought he was going to get. At both tables, however, opening leader thought the second double canceled the first. Both doubled slams were made for an unusual flat board.

You will be OK on this hand if the spade finesse works and trumps aren't 4-0. You just need to handle the entries correctly. Win the lead in hand and play the ♦Q from hand and the ♦K from dummy. If it holds, draw trumps via the finesse and set up a diamond for a heart discard with the ♣A as an entry to reach the diamond winner. If the first diamond is taken by the Ace and a heart comes through you rise with the Ace, cross to dummy and take the trump finesse, later pitching your losing heart on the winning diamond.