Live and learn! I did some carriage returns in the url links, and it made a mess of the hands. I had not noticed this, but now I think I have it right.
I will edit this more later.
I thought there were several points of interest. Mostly I will look at the play. In my opinion, far too much time is spent looking at bidding, too little looking at play.
You are in 3NT, bidding not shown.
http://www.bridgebase.com/tools/handviewer.html?sn= &s=SAHQT3DAK82CAK865&nn=&n=SQJ765H854DQJC972&d=n&v=b&b=7&
This could be a challenge.
Now with the bidding:
http://www.bridgebase.com/tools/handviewer.html?sn=&s=SAHQT3DAK82CAK865&nn=&n=SQJ765H854DQJC972&d=n&v=b&b=7&a=PP1CP1SP2NP3SP3NPPP&
After 1C-1S I would have reversed into diamonds. But the final contract will probably still be 3NT.
Now with the opening lead
Heart 2,4,7,T
Claim. Ok, not quite. But assume the hearts were dealt as 4-3. This is indicated by the lead of the 2. Also. if the lead were from AKJ92 then W might have bid 1H over 1C on the first round of bidding. Anyway, people get dealt 4 card suits more often than 5 card suits. All in all, it is reasonable to expect hearts were dealt 4-3. So assume neither opponent started with five hearts. Now we can establish nine tricks:
The play:
Heart to the T on the lead
Ace of spades
Small diamond to board
Queen of spades
You have now established 9 tricks: 2 spades, 1 heart, 4 diamonds, 2 clubs. 2+1+4+2=9.
They have taken 1 spade and unless the hearts were originally 5-2 they can take only three more hearts.
West's holding included the AKJ2 of hearts. Leading the 2 would be right if East held Qx, but perhaps on the bidding it is more likely that the Q is with South (as it was).
Suppose W starts with the heart K and gets a discouraging card from E. A shift to the spade T will set this, or it might. The plan is to get to East's spade K and have a heart come through.
There are two ways declarer might survive after the heart K is led. W will switch, but might switch a diamond instead of a spade. Or, if he plays the spade Ten at trick 2 declarer could cover and hope East errs by playing the K. Let's assume the latter. So:
King of hearts at T1
Spade TJKA at T2.
Are we home yet? No, not really. We now have 2+0+4+2=8 tricks in plain sight. We need another. This can only come from clubs. So we want to duck a club. But if E wins the club, a heart through will give the defenders one club and four hearts for down one.
A little bit of avoidance play is needed.
Go to the board with a diamond and lead a club, If E plays the 3 or 4, play the 8. If instead E plays the Q, J or T, go up, return to the board with the other diamond, and lead another club. As the cards lie, this works out.
Let's look at all four hands.
http://www.bridgebase.com/tools/handviewer.html?sn= &s=SAHQT3DAK82CAK865&wn=&w=ST983HAKJ2D764CJ4&nn=&n=SQJ765H854DQJC972&en=&e=SK42H976DT953CQT3&d=n&v=b&b=7&a=PP1CP1SP2NP3SP3NPPP&
As you can see, to beat 3NT we have to get E in with a spade.
Heart K
Spade T, E playing signaling encouragement but not covering the Q/J if played.
I would say this is a pretty tough defense to find.
Which is not to say that, looking just at the NS hands you want to be in 3NT.
The bidding. If I were playing NS with my clone it would begin
1C-1S
2D-2H
The 2D call shows five clubs and four diamonds, and a big hand.
The 2H is a sort of Lebensohl bid, potentially showing a weak hand.
After this, S has more than s/he has yet shown. A 2NT call can now be passed. This is a matter of judgment. I suspect I would bid 3NT, based n the extra strength and on the ten of hearts. They can beat this, but it is not what I would call obvious and so this might come in.
Summary:
After the lead of the small heart, the hand can be made, and the winning line is, I think, pretty clear.
The hand can be defeated, but the defense is not obvious.
If W starts with the heart K and then either plays a diamond or if it goes spade TJKA, then the hand can be made by ducking a club, but care must be taken to make sure the club iis ducked to W.
Some points where agreement is needed:
If W at trick 1 is to lead a high heart, I believe the broad consensus is that the lead of the A would ask E to drop the Q if s/he has it and to show count otherwise, while the lead of the K asks E to encourage with a high honor (but not to drop it). I believe some people reverse these agreements.
After the reverse sequence 1C-1S-2D, most play the 1C-1S-2D-2H call as artificial, indicating a hand the is usually not interested in pursuing game and that 1C-1S-2D-2S is forcing, shows a fifth spade, and might or might not have extra values.
