2♣. Your partner opens 1♠ and South overcalls 1NT. South has shown a strong balanced hand (15-18) so the meaning of your bids change. Most strong hands will double for penalties, which leaves two-level bids as weak and competitive: non-forcing. Your hand is suitable for a natural competitive 2♣. Any hand that thinks it can make game in this auction is probably going to start by doubling 1NT and expecting to get it a lot off. All other hands are wanting simply to compete for the part-score, which is why you should use all the 2-level bids for this reason. This hand should be a battle between diamonds and clubs.

East Hand ♠ AK543 ♥ QJ2 ♦ T9 ♣ K52

Pass. Your partner opens 1♠ and South overcalls 1NT. You have no long suit and you cannot be sure your side has the majority of points, so you should keep quiet. A double of 1NT would be for penalties, for which you are slightly too weak; 7+12 is only 19. As it happens on this hand, you do have 20 points between you, 
 but you cannot be sure of getting 1NT down. With no support for your partner and no long suit, you have no choice but to pass and hope you might defeat 1NT. 

East Hand ♠ AK543 ♥ QJ2 ♦ T9 ♣ K52

Double. Your partner has made a penalty double of 1NT, so you should be on the lookout to double again, aiming to hunt them down and get a good penalty. To double at low levels your side needs the majority of points and good trumps. You place your partner with about 16 points for his double so adding your six, you have the comfortable majority of points and your diamonds are excellent, so you should go ahead and double again. After one penalty double all subsequent doubles are for penalties, so your partner passes and you collect a healthy score.

East Hand ♠ KQ43 ♥ AK2 ♦ J7 ♣ A876

Pass. This is an interesting situation: you have opened the bidding and then the bidding returns to you after North overcalls. This is very different to the situation when your partner has responded. You had planned to rebid 1NT, but that is based on the fact your partner has shown 6+ points. Here, your partner has done nothing so he may well have no points. You need to be careful in this situation – if you bid 1NT, you might find yourself being doubled and giving away an unhealthy penalty. A 1NT rebid should be much stronger in this situation; showing 17-19 points. With just 15 points you should leave your opponent in 1♠, happy to have length in his suit. North-South do not have much of a spade fit, but they do have plenty of points. Leaving your opponents in 1♠ is much better than going off in a contract of your own.

East Hand ♠ T97 ♥ T2 ♦ Q532 ♣ 7653