Given the bidding and lead, you can be certain that West holds the ♠A.  In that case, success is assured.  Duck the ♦10 in both hands.  Win the next trick, draw trumps and ruff a small spade in hand.  Then ♦A, ♦K and the ♠Q discarding a small club will put West on play, forced to lead a club or give you a ruff and discard.

If you cover the ♦10 with the ♦J, you might not be able to deny East a diamond entry to play a club through you.

On the actual layout of the cards, you can still succeed if you do play ♦J at trick 2.  You win with the Ace and later play the ♦6 from hand, ducking if West plays the 8 or 9 and rising with the ♦K if West plays low.  This line would fail however if the diamond suit was less favourable for declarer.

You will need the trumps 3-2 to stand a chance so assume that is the case. Two spade finesses are decent odds, but you have the additional chance that West started with ♦KQx. Win the first trick and run the ♠J (12 tricks if it is covered). Suppose West wins and exits with a club. Win in dummy and ruff a diamond. Two rounds of trumps finishing in dummy allows you to ruff another diamond. If the ♦Q hasn't dropped, cross to dummy with the a trump to try a second spade finesse.

Clearly either finesse might lose, but there are two reasons to steer away from the (auto-pilot) spade finesse.  The first is that if it fails your chance of dropping the club king is too remote and you will be held to five spades, two hearts and the ♣A for down one.  On the other hand, if the club finesse fails you have the chance of dropping the spade queen which would see you home with six spades, two hearts, and two clubs (or one if they cash their diamonds).  The second reason is that if the spade finesse succeeds you are still not home, as there might be ♠Qxxx onside and you still have to lose a spade trick; while a successful club guarantees the contract.

Justice is served if you take the club finesse, as that is the one which works and you can now clear the spades. 3N making!

Hands like this are common in card play problems. If you duck a heart early you can test the hearts and if they don't break, you fall back on the club finesse. Well on this deal, you need to be aware of an extra chance. Suppose you find that East holds 4 hearts. Now you can cash the spades and one top club and all the winners in dummy. if East has kept his heart guard, as he must, then he will have had to come down to a singleton club. Therefore you don't need to bother with a club finesse as the ♣Q will fall anyway. This is called a show-up squeeze. No special counting is required - merely to know that East's last card is a winning heart.

This is a very straightforward hand. If the club finesse loses you will be down for sure. Suppose you win the lead and draw trumps finishing in dummy. Now you can run the ♣T and take a second finesse. That will be OK if clubs break but you will be down if they are 4-1 as you have to win the second club in hand. You can circumvent this by thinking ahead. Win the opening lead and play a club to the Queen. When that holds, you revert to the earlier line  The difference is that you can now take 3 club finesses and pick up the 4-1 break.

You need to take an avoidance finesse in diamonds to keep East off lead so that you don't suffer a spade through. However, you need to be careful. If you cross tom dummy with a heart and play a low diamond to your Knave, you will go down. The winning line is to lead the ten of diamonds from the table on the first round. If this is covered, you return in hearts to play a diamond to your 8.

The key play is to not cover the jack of hearts, making it impossible for the defenders to continue the suit, at least not immediately.  So play low from dummy and win with the ace in his hand. If the club finesse is onside, 4S will be cold.  If it is offside, the club suit will be good for a discard.  But first, you must draw trumps.  It takes three rounds to do this, East having the three.

Now lead the ♣ J.  In practice this runs to the King.

Is South going down now?

Not yet.  Since you still have the queen of hearts in dummy, the defence cannot cash 2 heart tricks at this point.

East returns a diamond after taking his king of clubs.  Now you must not finesse as if it loses, West is in to fire a heart through dummy.  Instead, rise with ♦A, cash the clbs to dispose of a heart loser, and then concede a trick to the ♦K.  This way you make the contract even with all 3 Kings wrong.

Declarer won the opening lead with the ♠K over North's ten and led a club to dummy, followed by the ♥Q.  This was ducked all around and a second heart was won by North, who exited with a low spade.  Declarer was quick to seize on this misdefence when he finessed the ♠9.  East was then able to cash 4 more black suit winners so that 5 diamonds in total could be discarded from the table.  A diamond to dummy's Ace was followed by a trump.  South won the Ace but had only clubs left.  The forced club lead allowed declarer to ruff in hand - discarding dummy's last diamond and so trick 13 was made by ruffing a diamond on the table.  Well played!

The first thing to realise is that playing on Clubs is doomed to defeat as the defenders will have the A♣  and at least 4 spades to cash. You can make this contract if the heart finesse succeeds, but need to guard against West holding 4 hearts. Take the ♠A and the ♦Q. Now overtake the ♦J and finesse the heart. If thet wins you overtake the ♦T for another heart finesse and then yoiu have another diamond entry for a third heart finesse.

Jack points out :  If East has 9xxx in diamonds and a doubleton heart, then they need to make sure they play the ♦9 when declarer leads the ♦3 from dummy on the third round of the suit so that declarer can't use the ♦8 as an entry to hand!

If the spade finesse works you will be home barring a 4-0 break, but you can improve on this chance. You have the entries to set up the heart suit provided it breaks no worse than 4-2. Win the lead in hand with the Ace and play Ace and another heart, ruffing with an intermediate trump. If an opponent shows out on the second heart, then you will have to play for the spade finesse to be right. Assuming both follow to the second heart, you can now play a low trump towards dummy.. It doesn't matter whether this wins or loses, you have a trump entry and a club entry to set up the heart suit, and the ♦A to get there to enjoy a diamond discard.

This is a hand where finesses abound, but if you play correctly, the hand is a sure thing. If East gets on lead, the defence might prevail with 4 diamond tricks. Cross to dummy with a club and finesse the ♠9. Let's say that loses to the knave. If West leads another diamond he gives you your ninth trick so say he exits passively. Then you cross again in clubs to finesse the ♠T. Even if this loses, you have established a second spade trick to bring your total to 9. Note that it is not good enough to cross to dummy at trick 2 with a heart as then West can play a second heart when he wins the first spade and then ultimately get his partner in for the killing diamond lead.

Rather than take a heart finesse, you should first cash 10 winners outside the heart suit. On the eleventh trick, dummy is down to ♠J,♥AQ. West is known to hold the ♠Q from his opening lead, and he has to keep this card to prevent you scoring the ♥A and ♠J. You throw the ♠J and then play a heart. If the King does not appear, you play the Ace and will succeed in dropping the King when the layout is as shown. In effect, West is squeezed, for although he holds nothing in hearts, his discards have to give you the count in the suit. 

It look tempting to cross to dummy with another spade to repeat the club finesse, but there is a danger in this. If West has ducked holding the club king, he can win the second round and play another heart. East can duck this trick and leave you stranded in dummy, forced to concede  five further red suit tricks. You can avoid this by refusing a second club finesse. Just continue with 2 more rounds of clubs, discarding the heart from dummy. Now if the defence plays hearts, you have the entry to hand to cash your clubs, and if they dont play hearts, you have the time to set up the diamond suit, losing no more than 1 heart, 1 club and 2 diamonds. 

If the club finesse works then you will have no problem, so can you cope if the finesse is wrong? If East wins a club and switches to a diamond, you will be defeated if West can ruff the third round of clubs and cash a diamond. The solution is to play to the King of clubs and then back to the Ace before leading a third club. Whenever clubs are 3-2 or 4-1 with West holding Qxxx, you are a tempo ahead.

If hearts break and the club finesse is right you have 12 tricks, but if you can make 3 spade tricks then you won't need the club finesse. Win the lead and cash 2 top hearts. If the suit doesn't break then you will need a favourable position in both black suits. If both follow to 2 hearts then play a low spade (not the ten) towards dummy. If an honour appears on your left then you have the 3 spade tricks you need to fullfil your contract. If West plays low then finesse the 9. If this loses (as it probably will) then subsequently take 2 finesses in clubs. If West started with both spade honours then the 9 will hold and you can afford to lose a club trick.

Diamonds will provide you with the extra tricks you need but the obvious danger is that South will wijn a diamond and fire back a heart to North's winners. You can give yourself a slight extra chance by laying down the ♦A and occassionally dropping a singleton King in South. However, a better line is to cross to dummy with a club and finesse the ♠9. Say North exits with a diamond. You win the Ace and play off the ♠K before crossing back to dummy in clubs to take the ♠A. If both spade honours have fallen, you are home without risking the diamond King being guarded in the South hand.

The odds in the trump suit played in isolation favour a finesse for the Queen, but you should consider the hand as a whole. If you take a losing finesse, you will be down immediately, but if you play off the top hearts you may have a chance to discard all of your club losers before an opponent can ruff in. Suppose you lay down the top hearts and both opponents follow but no Queen appears - now what? It looks tempting to first cash the diamonds and then follow with the spades and hope that the hand with the last trump has 3 or more spades, in which case your club losers all get thrown. However, this line of play is no good. You always need the hand with the last trump to hold 3+ spades, so you may as well play spades first. This scores on the layout shown when you are able to play 5 rounds of spades discarding all your club losers. Of course, if spades had broken 3-3, you would have had to try for a diamond discard before leading a fourth round of spades.

On this hand, you ideally want to set up the clubs before being forced to take the heart finesse. To this end, cover the opening lead with the ♦J and discard a club from hand. You can later discard another club on the ♦A. There are enough entries to dummy to set up the clubs by ruffing and get back to cash them without having to resort to the heart finesse.

This hand hinges around the play of the trump suit. You have a standard safety play available to guarantee no more than one loser if the suit happens to break 4-1. You can achieve this by playing off the ♥K and later playing a heart towards the Jack. If either hand holds ♥QTxx they can be restricted to one trick in the suit. However, we don't know initially whether we can afford the safety play. We would look very silly losing an unnecessary heart trick if we also have a club loser. The best line is therefore to win the first spade in hand and finesse the club. If it holds we then make the safety play in hearts. If the finesse loses we need to play hearts for no loser and the best way to do that is to sart with a finesse of the Jack as this picks up any 3-2 break with West holding the Queen and also a singleton ♥Q with West. Playing the Ace first to drop a singleton Queen with East does not help as you will still have to lose a heart trick to West's ten.

At first glance it looks like this contract depends on finding the ♥A or ♦K onside. However, you can improve your chances. From the lead it is likely that West holds the ♣Q so win the lead and cash the other top club. Now a trump to dummy allows you to lead the ♣J from the table and discard a diamond from hand. West will win and probably lead a fourth club for East to ruff. You overruff and draw the last trump before taking a ruffing finesse in diamonds. You only lose the lead to the safe hand and will be able to discard a heart on a diamond, losing at most 1 club, 1 diamond and 1 heart.

The problem is to set up the clubs for 2 spade discards. Finessing the queen gives the best odds. So draw trumps, club finesse, cash the Ace and ruff a club. Now back to dummy with a trump to ruff the fourth club. If clubs have broken, you are home; if East had 5 you could pick up his Jack via a known ruffing finesse on the fourth round. If West turns up with 5 clubs then run all your trumps and hope West has the ♠K, in which case he will get squuezed in the black suits.

You have 3 tricks outside trumps and even making 6 trump tricks leaves you short. The obvious source of extra tricks is diamonds but do you finesse the diamond Jack or do you try for diamond ruffs?  If you play carefully, the contract is assured if 2 rounds of diamonds stand up. Ruff the third diamond with the ♠A, return to hand with a club ruff, and ruff your last diamond with the ♠7. The ♠Q will be your only loser.

There is a danger that East will gain the lead in hearts at some point and play a diamond through your King. You might then lose a heart and 3 diamonds. The best line is to duck trick one. Suppose West switches to a heart. You win the Ace and discard your second heart on the ♣A. Now 2 rounds of trumps with Ace and King will clear the trumps even if they are 2-0. You can lead and pass the ♥J, discarding a diamond if East does not cover. This may lose but you have 2 more trump entries to dummy to try a second ruffing finesse in hearts. 

Given the spade suit in isolation, the odds play is to finesse. Of course, you need to consider the whole hand. If you play clubs yourself you will most likely lose 3 tricks, whereas if the defenders lead the suit, you can restrict your losses to 2 tricks. This points the way to your play in the spade suit. Rise with the ♠K. Suppose West follows small. Then you just eliminate the hearts and then the diamonds and exit with a trump, endplaying whichever opponent wins the trick. If the ♠Q drops under the King, you lose no trump trick but ultimately lose 3 clubs. So refusing the spade finesses secures the contract whenever spades are 3-2.

It is likely that West holds the ♥Q, so that a later heart finesse will see you home. However, you do better to win the ♥A and play off the King of diamonds. Let's say East follows. Now you can be certain that West holds the diamond suit and so if he also holds the ♥Q, he will be squeezed on the run of the spades. When he discards down to one heart in order to keep a diamond guard, you can be sure that the ♥Q will drop on the King whoever held it originally.

You ruff the opening lead in dummy. There will be no problem if the trumps break 3-2 but otherwise you might lose a trump and multiple diamonds. You can safeguard against this by cashing the ♠A at trick 2 and continuing with a spade to your ten. If it holds you will make 12 tricks. If it loses, West cannot take more than one diamond trick so you will make your contract.

In dummy with ♥A, you must immediately play on clubs. ♣A, ruff a club high, ruff a heart, ruff a club high. If clubs have broken, you have one more shot before resorting to the spade finesse. Lead the ♦T to the Queen in dummy. If the 7 drops, you can ruff another club high and re-enter dummy with the ♦6 to then throw a spade on the established club.