Firstly, a note on the bidding.  North should not bid 6NT over 6.  Partner is showing a highly distributional hand suitable for a small slam in either major and not a hand where North should compete to 7!  Competitive bidding should be saved for use against your opponents.

West leads the K.  What is the best line?  Firstly the trump suit must break 3-2 or there must be a singleton J.  Given this the hand then comes down to finding the Q, since even if the finesse works you will not be able to discard enough losing s unless the suit breaks 3-3.  The finesse is only 50%, since you have no information as to the shape of the defender's holdings and no real prospect of getting an adequate count.  Is there anything else that can be done to improve your chances?  The suit is the key.  If the K comes down in three rounds or less then all the losing s can be discarded on the established s, provided that the suit breaks no worse than 4-2.

Win the opening lead with the A, discarding your from hand!  Cash the K to check whether a singleton Jack appears and then ruff a low .  Cross to the Q and ruff a second low .  Draw the remaining trump(s) and cross to dummy via the K.  If the K has not already appeared, lay down the A and hope that the suit breaks 3-3 and that four rounds of s can then be discarded..  If the K doesn't fall under the A, there is still the option of taking the finesse.

West leads the 10.  At first sight the hand looks relatively easy but a review of the play as it actually occured will highlight the difficulty.  Declarer ruffed when the Q was covered by the A and switched to the K and continued with a second trump when this was allowed to hold.  East took the Q and switched to a .  Declarer played the Q and West continued the good defence by ducking.  Now declarer was defeated, since he could not get to the dummy to take the  finesse.

To make the contract declarer must think about his entries before playing to the first trick.  He should recognise that this is a dummy-reversal hand and ruff the opening lead with the Jack (or King).  Now a low trump to the table forces East to win the first round.  A second round of s will be ruffed with the K and a second low trump led to the table.  No defence can prevent declarer gaining the one entry to the dummy so that the critical finesse can be taken. 

Not the greatest slam that's ever been bid, with a loser in both the trumps and spades to contend with.  However, the opening 3C pre-empt by West raises the chance of an elimination play.  After winning the Ace of clubs, ruff the second club immediately.  Cash the King of trumps (it goes without saying that you take careful note when West follows with the 9!)  followed by the Ace and King of spades.  Cross to the Ace of diamonds and play a second diamond to the Queen.  If both opponents follow suit you are almost home.  Switch to a trump and run it if East plays low.  When West is forced to win the Queen he can only return a club, allowing you to discard your losing spade and ruff in the dummy.  When a diamond to the King holds the trick you can draw the last trump and claim.

Can West rescue himself from the endplay by playing the Queen of trumps under the King?  A good try, but unsuccessful since declarer can now squash the 9 by running the 10 of trumps or can revert to the line above by running the 8 and only playing the Ace if East covers with the Jack.

After South passes, West opens a weak 2, showing a six-card suit and 6-10 HCP.  North passes! (not good, since he should be willing to compete to at least 3).  East passes and South protects with 3.  Thinking this shows a six-card suit, North raises to game.

West leads the K.  Clearly East has only a singleton spade and ducking would be a disaster.  Even if the trumps break 3-3 there is a certain trump loser and there is also at least one diamond to lose, since West will cover the Queen should declarer attempt to run it.  Declarer also has to find the Queen.  On top of all this, declarer cannot afford to let West back in too early, since otherwise he will lose two more spade tricks. Ugh!

Clearly the only hope is to discard losing spades on the established diamonds and this can only be done if West does not get in first.  Therefore the only hope is to play East for the  King.  So win the first spade and switch to a low diamond immediately.  East takes the King and continues with a second diamond.  Crossing to the Ace of trumps, declarer cashes the  Ace, discarding a losing spade.  All follow (phew!).  Now declarer switches to a second round of trumps, ducking if East plays the  Queen.  A club switch is taken in hand with the Ace, since declarer still needs a guaranteed entry to the dummy.  The remaining trumps are drawn - all follow (phew!) and eleven tricks are wrapped up when declarer crosses to the dummy via the King and cashes the last two diamonds, discarding his remaining black cards.  Well played.

If you think that was a challenge, try out Test Your Defence (4)!

West led the 7.  Declarer rose with the Ace and ran the J to West's K.  A second spade was ruffed and two more trumps were drawn, ending in hand.  The Q was run to East's K and now the K of spades defeated the contract, since declarer could not ruff without establishing a second trump trick for the defence.

There are a number of lines to make the contract, but the most straightforward is simply to duck the first spade.  A trump switch (best) is conceded to West's K and a second spade is taken by the Ace, with declarer discarding a losing diamond from hand.  The remaining trumps are drawn and declarer then switches to the Q, running it to the K when West follows low.  Now declarer still has the last trump to ruff a spade return, with no losers remaining in the minor suits.

After South opened with a pre-emptive 3, North's raise to game was automatic.  West led the J and it was almost instinctive to cover this, but on this hand it proved to be a serious error.  East took the Queen with the Ace and promptly switched to a spade.  West won and cashed a second spade and then switched to a diamond.  Once the diamond finesse failed, declarer was defeated.

This debacle could have been avoided if declarer had simply ducked the opening lead in dummy.  East can still win the Ace and switch to a spade, but now declarer can rise with the  Ace on the first round of the suit, draw the trumps and discard two losing diamonds on the established K Q.

If East does not overtake the J, declarer can still afford to go up with the Ace if West switches to a diamond.  After drawing trumps, declarer takes a ruffing finesse against East in clubs.  If East ducks the K declarer discards a losing spade, thereby reducing his losers to one spade, one diamond and one club.  If East covers the K, declarer ruffs and returns to dummy with a trump.  The Q is cashed and a spade discarded to restrict his losers to the same three tricks.

Playing 4-suit transfers, North/South's only means of showing an invitational raise was to go via Stayman.  After the lead of the 3, declarer must establish the diamonds before taking the finesse of the Q.  If you do not establish the diamonds before burning your only sure entry via the A, whichever defender holds the A, will simply duck the first round of diamonds to deny entry to the table.  A straightforward hand, you might think, but a good player got it badly wrong. 

West led the 10 against 6NT.  Sometimes you get into the wrong contract and need some pretty nifty footwork to rescue the situation.  6 or 6 are both far better contracts than 6NT.  Whatever the rights and wrongs of North's positive response of 3 over 2, South should have paid more serious attention to his partner's attempts to show a long club suit and a hand shape that was not suitable for no-trumps.

The contract appears to rely on a successful finesse of the Q but cashing the K and finessing on the second round dooms the contract (losing a club, a diamond and at least one spade.)  However, if declarer finesses the Q before cashing the King, East cannot afford to take the first round since this will allow declarer to overtake the King and run the clubs to dispose of four losers (three spades and a heart) to make his contract.  Thus East must duck the J and declarer now switches to the 9, running it if East plays low.  Regardless of whether West holds the K, the location of the Jack has been revealed.  Game over.  (If West wins with the J, declarer will win the return and then overtake the K.  If the Q does not fall now, declarer still has the chance of playing for divided spade honours and finessing the King.)

Why is this the best line?  It keeps all your options open while giving the opponents every chance to go wrong.  How many players sitting East would actually have the courage to duck the first round of clubs, after all?

Declarer correctly elected to duck the spade lead to the Queen.  The spade 7 was covered by the Jack and ducked by West.  When none of the suits broke declarer had only 8 tricks and had to concede defeat.  West still had to defend carefully when declarer played on the hearts.  If the Ace of hearts had been cashed after the minor suits had been tested, West had to be careful to unblock the Jack.  If he had not done so, he would have been end-played on the second round of hearts and East would have been unable to overtake without conceding the ninth trick in hearts.  If declarer had underled his Ace of hearts on the first round of the suit, then West could rise with the Jack and cash his master diamond (East discards his losing heart) before exiting with a heart.  Now it makes no difference if declarer takes the second heart, since he must exit with a third heart to East, who promptly cashes his Jack of clubs for the setting trick. 

Unlucky certainly, but also poor play.  Declarer should have recognised the possibility that none of the suits would break and given himself the extra chance of success.  The spade suit should have been unblocked by playing the Jack under the Queen.  East will switch to another suit rather than give a free finesse.  Now declarer can test the two minor suits and, when neither of them break kindly, he has still retained the option of the successful finesse of the 10 to make his contract. 

New Year resolutions tend to be broken quickly at the bridge table.  When West led the Jack of hearts, hoping to find East's shortage.  Declarer lost no time in breaking his resolution to think before playing to the first trick.  He followed low from the dummy and captured the King with the Ace.  The King of trumps was taken by the Ace and now the 10 of hearts killed declarer's chances.  No matter what he did, he could not avoid the loss of three heart tricks and the Ace of trumps.

Declarer should simply have ducked the King of hearts.  No matter what East returns the contract cannot be defeated.  When West gets in with the Ace of trumps, the return of the 10 of hearts can now be run to the Ace.  If East ruffs ahead then declarer can claim, conceding two heart tricks and the Ace of trumps.

Ah well...there's always next year!