A 4 (splinter) is the best response over a game-forcing 2 response.  The hand is a graphic illustration of the merit of splinter bids.  When North splinters he is agreeing s and showing a singleton or void in s.  It should not be difficult to assess that North's values are in the suit and that therefore 6 must be a viable contract.  When North showed one control in response to South RKCB 4NT, South bid the slam.  Without the splinter it is very difficult to get the information required at a level low enough to explore the slam.  If North had rebid 3 instead of 4, a 4-5-5-5 cue-bidding sequence could still leave a loser in both s and s from South's point of view.  North would need to take a very positive view of South's trumps and s to raise a 5 sign-off to 6.  Certainly most of the pairs in a recent duplicate found it too difficult, since only one pair in thirteen managed to bid the laydown slam.

It is tempting to bid a 'fourth-suit-forcing 2S over 2D, but this could give partner a problem if he holds something like 2-2-4-5 shape with two small spades.  A 2S rebid says nothing about your hand and it is important to tell partner that you want to play in hearts even if he has only two of them.  Therefore the correct bid over 2D is to jump to 3H, forcing to game and telling partner that you have at least a six-card suit.  Partner will raise to 4H and you will then follow up with 4NT (Roman key-card Blackwood).  When partner is able to respond with 5S, showing two controls and the Queen of trumps you have identified 9 of his 16+ HCP's.  You can either ask for missing Kings via 5NT or settle for the grand slam in hearts straightaway.  There are 17 tricks available in 7H (Ace of spades, spade ruff, seven hearts, four diamonds and four clubs) and only 16 in 7NT (no ruffing allowed, alas!) so it should not be difficult to make either grand slam.

5 is correct!  South's 4 initiates a cue-bidding sequence and promises at least one of the top two honours in the trump suit (i.e. hearts).  It should be obvious that partner requires very little more to make a grand slam in hearts viable - either the K and/or Q or compensatory shortages in either suit.  Your response of 5 shows second-round control in diamonds and one of the top two honours in trumps and all the missing first-round controls (see article 'Cue Bidding' in the Library).  If you reveal all the hands now you will see that South will respond with 5 over 5, prompting a 6 response from North with a (yippee!) 7 rebid from South, closing the auction.

Without the key bid of 5 there is not enough space to explore the grand slam.  Had North not been able to make this bid there would have been no chance to bring home the slam.  Note that the 5 cue-bid also denies second-round control in spades, since if North had held the K he would have rebid 5 rather than 5 and if he also held all four kings he would have jumped to 6 rather than 5 or 5.

What on earth is going on?  First (and most important) none of the players sitting round this table are complete idiots, so you should assume that they all have some valid reason for each of the bids they made. 

Partner jumped to 3 over East's overcall and also rebid 5 over East's 5.  The clear message from partner is that the contract belongs to your side and that no sacrifice by the opponents will compensate.  You know that partner has a long (8+) and completely solid spade suit and probably two-card diamond support.  Therefore he holds a maximum of three cards in hearts and clubs.  The most revealing bidding is East's, of course.  A 2 overcall, followed by a 5 rescue of 4 doubled and finally a 6 sacrifice over South's 5.  Clearly he holds eight clubs for the 5 bid (and should have overcalled 5 over 1) and at least a nine-card suit for the 6 bid.  Therefore either South or West or both are void in clubs. 

If this reasoning is solid, it could be crucial that South should play the hand rather than North, since East might well be able to lead Ace and another club, which could feasibly create a trump promotion for one of the defenders.  It is also clear that South's spade suit is pretty solid, headed by A K Q at least.  Therefore 6 must be at least as good a contract as 6 and the grand slam in 7 is even better!!!

Think about it.  Partner holds 8 (or 9) solid spades, 2 (or 3) diamonds, void or singleton club and void, singleton or doubleton heart.  Thus all his losers can be discarded once the trumps have been drawn.  In for a penny...

So what do you think of the auction?  Pretty barmy really, particularly by West.  But precisely this hand and the subsequent auction to 7S occurred in a major congress a few years ago.