(1) 1NT = 3-card support, forcing. Not alerted.
(2) 2♦ = not discussed.
NS system: 5-card majors, 15-17. With 4 spades and 5 diamonds, responder would bid 1♠ unless he had a game-force. Facing a natural 1NT rebid, 2♦ would have been an artificial game-force.
South bid 4♠, reasoning that:
- This is equivalent to a support double sequence.
- In such sequences, "everybody" plays a bid like 2♦ as a signoff with only four spades. If that's what North has, 3♠ is impossible, so South knows that a misunderstanding has occurred.
- If North had an invitational hand with five spades and four diamonds, he would never risk an undiscussed 2♦ when he could bid an invitational 3♠.
- If North has an invitational 4-5, 3♠ says that he now wants to bid game, and suggests playing game in the 4-3 fit. This hand is well-suited to that.
- There are two similar sequences (see below) which suggest that the partnership would not bid 2♦ with five spades.
Would you allow the 4♠ bid?
Two potentially relevant auctions where NS did have agreements:
(a) Uncontested 1♣ - 1♥ (transfer); 1♠ (3-card support):
- 2♣ = artificial, invitational, only 4 spades
- 2♦ = artificial, game-force
- 3new = natural game-try with five spades
- 3♠ = invitational with five spades
(b) Uncontested 1♦ (5 cards) - 1♠; 1NT (3-card support, F1):
- 2♣ = artificial, invitational+, only 4 spades
- 2♦ = signoff
- 3new = natural game-try with five spades
- 3♠ = invitational with five spades

Help

1♥ pass 1♠ dbl
1NT(1) pass 2♦(2) pass
3♦ pass 3♠ pass