NS play Benjamin Acol, weak NT.
2♦ = 23+ balanced or any GF (A)
2♥ = relay (A)
2NT = 23-24 balanced
3♥ = transfer to spades (not alerted)
4NT in other circumstances could be quantitative or RKCB, but it's difficult to believe that South would want to make a bid with either of these meanings in this auction, or indeed to make this bid at all. 5♦ would show one keycard in response to RKCB.
What options can North ethically choose here, given South's failure to alert 3♥?
Problem 2: Matchpoint pairs, love all, dealer W.
EW play one-of-a-suit openers as natural and forcing (except that 1♣ could be only two cards in a 15+ balanced hand), 5-card majors, always 14+ except that 1M could be 11+ with four cards in the other major. 12-14 NT, opening two-of-a-suit 10-13 natural, at least 5-card suit, unbalanced.
1♥ = 5+ hearts, forcing, either 14+ or 11+ with 4+ spades (A)
2♣ = GF [edit: unless partner rebids 2♦], either natural or strong and balanced or heart support (A)
2♦ = artificial, promising 11+ and 4+ spades (not alerted)
2NT = relay, asking for more information on shape (A)
3♥ = extra length in hearts
3NT = to play
The general agreement here is to ignore the opposition's double, and both players agreed later this was the correct system bid. Can West rebid the heart suit after East failed to alert 2♦?