At imps, your play is clearcut.  Since you are taking the diamond finesse to West, the correct play is to rise with the ♠A at trick 1 and finesse the diamond.  If this loses West may well continue with another spade or a heart giving you 11 tricks, but in any case 10 tricks are now assured.  If you get too greedy and run the spade at trick 1, East will win and switch to a heart.  Now when the heart finesse is wrong you finish up 2 down when the ♦K is offside.  At pairs, you might risk running the spade, and could finish up making 13 tricks if everything is right for you.  The choice is yours!

If a lead looks like a doubleton and smells like a doubleton, it probably is a doubleton.    Why would anyone lead from an AQ into a notrump bidder?    Win the ♦K and assuming a 3-2 trump division, draw trumps and exit with the  ♦J.   Note:  When the adverse trumps are 4-1, a long suit is usually led.

East, on play with the ♦Q has an unhappy choice of plays.    If East elects to exit a heart, play the queen and if it is covered, you are reduced to the club finesse.    If East exits a club, the most you can lose is a heart.    If East exits a diamond, ruff in your hand and discard a heart from dummy.    You now have to play clubs for one loser.    The best play is low to the king, low to the ace and then low to the jack if the queen hasn't appeared.

You have to bring in the clubs and still keep control of the hand.    Best is to play the ace-king of clubs and ruff a low club with the ♥ A.  Next, return to your hand with a trump and play the KQJ of hearts. If hearts divide 3-3, you have the rest. If hearts are 4-2, play winning clubs and the most you can lose is two diamonds and heart.   Yes, if clubs are 3-3 and hearts 4-2, you lose an overtrick, but this is IMPs and making the contract is far more important that risking your contract for an overtrick.   (If you draw four rounds of trump before touching clubs, in effect playing the hand at notrump, down you go.

Tip:

Ruffing a loser high when dummy has honor doubleton in trump, is a good way of unblocking the trump suit not to mention avoiding a possible overruff.

North's pass over 3♦  showed a minimum opening and denied three card heart support.

The diamond suit in dummy is threatening and it looks attractive to return a heart at trick 2 and then hold up the ♦A to cut declarer off from all those winners.  However, this is muddled thinking.  Partners lead is fourth highest or second from a bad suit.  If the latter, then declarer holds ♠AK, and would not have let you win the first trick with ♠Q.  Hence partner holds ♠AKxx(x) and you beat the contract quite simply by cashing ♦A at trick 2 and then reverting to spades.  Why is it important to play off the ♦A? - Well you may only have one chance to make a discard if partner has only 4 spades and partner may not realise of the necessity of a diamond switch when the layout is as above - always wrap partner in cotton wool when you can!

A little counting helps here. Declarer is marked with a singleton heart and four spades leaving eight "other" cards. Declarer's two more likely distributions are 4-1-5-3 or 4-1-4-4.  In the first case there is a danger that unless clubs are broached immediately, declarer will be able to draw trumps and discard a club from dummy on a fifth diamond. In the second case, partner has a doubleton club and may be able to obtain a ruff.

It is clearly right to overtake the partner's lead and shift to a low club, showing strength, at trick two. Your play works out beyond your wildest dreams because the are the unseen hands are as above:

As it happens partner wins the first club presumably with the jack, cashes the ♣K, and leads a club to your ace. Continuing with your sharp play, you play a 13th club and when partner uppercuts the ♠A out of the dummy with the ♠10, your J98 of trumps promote to the setting trick,

Tip:

When declarer turn up with an early singleton (hearts) and the length of at least one other of the declarer's suits is marked on the bidding (spades), consider the likely distribution of the remaining cards and defend accordingly.

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.

The best line is to win the ♠A at trick 2, draw trumps and start on the diamonds.  If one defender hold Axx he will hold up for 2 rounds as we have seen.  However, this means that so far you have not lost a diamond trick.  Now exit with a spade.  West has to win this trick and if he started with a doubleton diamond, the defence cannot cash the ♦A.  If West continues with a fourth round of spades, simply discard a diamond from hand and leave West on lead.  He will now have to lead a club - a lucky guess or West holding both club honours now sees you home.

BTW : the latests county newsletter came out yesterday.

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. 

You expect to make five clubs, five trumps, the ♠A and a spade ruff. The only worry is a 4-0 trump break (West cannot have four diamonds). As you expect West to hold the ♥A and entries to your hand are few, a little care is needed when the full deal is as shown.

After taking the ♠K with the ace, you should ruff a spade with the eight of trumps. Then, cash the ♦A and continue with the ♦10. Presumably, East will cover this with the jack. You will take this with the Q, cross back to dummy with a club and pick up East's remaining trumps by leading the ♦5 and covering East's card. Then, after drawing the last trump, you will have your 12 tricks.

You might play the ace and another spade, thinking you are getting rid of trumps, but that turns out to be an error.  West has the king of spades but he also has four of them.

If South continued a third round of trumps, West would win and lead another club.  That would force out dummy's last trump and West would now have the last trump and a good club.  That would result in down two. South still had chances but when he got around to leading his diamonds, West ruffed in on the second round. 

South does better to play spades in less hasty fashion.

Here is one possible line out of a couple that exist.  It might not be the best line but it shows how you might play when you fear a bad trump break.

Go to the queen of hearts and lead the queen of spades for a finesse.  It will win when West smoothly and correctly lets it win.  Lead the jack of spades.  East shows out, but you finesse again anyway.  West wins but South is in control.  If West leads more clubs, South ruffs and dummy has an entry plus good trumps and South can get the rest of the tricks.

Question:  What is the other line?

South, after ruffing the third club, can lead a low spade from his hand and can continue play along the lines shown above.

The main point is to show that 4-1 trump breaks do happen and sometimes can be catered to with careful play.

There appears to be a mass of tricks available on this hand, so now is the time to be carfeul.  There will be no problem if the clubs behave so assume you have a loser in the suit.  If you duck at trick 1, East will win and may embarrass you by switching to a spade.  Then if a club has to be lost, you may end up losing a heart, a club and 3 spades.  The winning play is to rise with ♥A at trick 1 and play a club to the Ace.  If either opponent show out on the first round of clubs, a low club towards the J will ensure 5 tricks in the suit and 9 in total.  The most the defenders can take are 1 spade, 2 hearts and a club.

As with all hands, counting your tricks and forming a plan at trick 1 is the key to success.

West's failure to overcall with 5 good spades surely indicates that he does not have a diamond picture.  Hence win trick 2 and play a diamond to the 7.  Let's say East wins with the ten and switches to ♥Q.  Win this and lead the ♦J from the table. When East covers with the Queen, you duck and West follows (as you hoped) with the 9.  Then you can win the next heart in dummy and finesse the ♦8.  This gives you 2 diamond tricks but also puts West under pressure.  If he lets go a club, you have 4 club tricks. If he keeps 4 clubs, he must have let go 2 spades.  Now you have 2 routes to success.  You can cross to dummy's ♣K and lead a spade, endplaying West.  Alternatively, you can just exit with a spade from hand, setting up dummy's ♠6 with the ♣K as an entry to cash it.  

The key to the hand is to appreciate that you need to find West with 9x or 10x in diamonds and play a low diamond to the 7.  This play is termed an intra-finesse. 

You have 10 tricks with 6 spades, 3 hearts and a diamond.  This is a time to be careful.  Suppose you ruff trick 3 with dummy's ♠8.  East may overruff and exit with a diamond.  This will leave you stranded in dummy, forced to try and cash hearts before trumps are drawn - bad luck, West ruffs the second heart and cashes a diamond for 2 down.

The solution to this hand is so simple.  Just discard from dummy at trick 3.  Then win the next trick, draw trumps and cash winners.  At the table, most declarers failed!

Overtake the ♠K with dummy's Ace and continue spades throwing the ♥K from hand.  If the defense continues hearts, you then have 5 spades, 2 hearts and 3 clubs for 10 tricks.  If they dont play hearts you can clear the clubs, losing at most 1 club, 1 diamond and 1 spade.

On the bidding, East is marked with most of the values, and your best bet is to hope he started with both black Kings and a doubleton spade.  Draw trumps in 3 rounds say and then play Ace and another spade, ducking in dummy.  If East started with Kx of spades, he will be endplayed to give you an extra club trick or a ruff and discard.

Looking at all 4 hands, can you see how the defense can prevail on an original diamond lead?

If East returns a low diamond at trick 2, West can win and switch to a club, destroying the endplay.  East might also have avoided the endplay by throwing the ♠K under the Ace, but unfortunately declarer can now finesse against the spades with West and bring home 4 tricks in the suit.  However, if dummy had held ♠QJ74 and West had the 1098x, this would have been a spectacular winning defense.