White (to play) is a rook down with a weak back row, so how did the 13-year-old force a win? Illustration: Graphic

Magnus Carlsen's world rating is now at an all-time high of 2881, 30 ahead of Garry Kasparov's peak and nearly 100 clear of Bobby Fischer's best mark. Yet chess fans continue to argue over which of the trio is the greatest.

Carlsen's often opaque playing style, with its emphasis on endgames and physical toughness so as to exploit mistakes after a long and tiring session, is one reason he has detractors. It reflects the change from four-hour sessions followed by an overnight adjournment to six or seven hours without a break and with speeded up play for the later moves.

He is a pioneer with this style, just like Mikhail Botvinnik, who maximised the depth of analysis during adjournments, Fischer, who knew his opening systems right into the ending, and Kasparov, who used his massive calculation skills to steer games into very sharp lines which he had prepared in advance.

The Carlsen grind superficially looks like sitzfleisch, using up time until the opponent weakens or loses patience. But he is technically very accurate, and the effect is gradually to reduce the opponent's options until he has to find a succession of only moves while also under clock pressure.

Defensive chess, resourcefulness under heavy attack, is another Carlsen speciality, as shown in his ninth match game with Vishy Anand and his escape from Hikaru Nakamura at Zurich. He is a mix of Anatoly Karpov, who specialised in technical endgames, and Emanuel Lasker, who made an art of provoking opponents into complex battles.

This is not enough for Fischer and Kasparov fans, who have a different idea of the gold standard for a true champion. One challenge for Carlsen is to win more games where he outclasses a top grandmaster, as he did against Anand at Bilbao 2012, or scores in a more tactical style. As this week's game and puzzle show, Carlsen was such a tactician in his youthful teens.

Even more, the super-champion gold standard is derived from tournament and match results where the legend demolishes the opposition with massive scores. It is represented inter alia by Paul Morphy's tour of Europe in 1858, Alexander Alekhine's record margins in 1930 and 1931, but most of all by Fischer's golden run, which included 20 successive wins, in 1970-72.

Can Carlsen confirm his 50-point rating lead by scoring similar results? The jury is still out. He will have at least three opportunities this year – at the elite tournaments in Azerbaijan in April and in Norway in June and at his first world title defence in November, for which it is reported that several Norwegian cities plan to bid – to cement his greatness and win over the sceptics.

Magnus Carlsen v Sergey Dolmatov, Aeroflot 2004

1 Nf3 f5 2 d3! d6 3 e4 e5 4 Nc3 Nc6 5 exf5 Bxf5 6 d4 Nxd4 7 Nxd4 exd4 8 Qxd4 Nf6 9 Bc4 c6 10 Bg5 b5 11 Bb3 Be7 12 0-0-0 Qd7 13 Rhe1 Kd8 14 Rxe7! Qxe7 15 Qf4 Bd7 16 Ne4 d5 17 Nxf6 h6 18 Bh4 g5 19 Qd4 1-0

Carlsen v Sipke Ernst, Wijk 2004.

White (to play) is a rook down with a weak back row, so how did the 13-year-old force a win?

3347 1 Qe5+ Kxf7 2 Qf5+! Ke7 (if Rf6 3 Qd7 mate) 3 Re3+ wins