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GM Viswanathan Anand is five-time world chess champion and has won world championship title in all formats. He played a pivotal role in getting India’s first ever Gold Medal in online Chess Olympiad 2020. Many believe – and with good reason – that he is a national treasure and the greatest sportsperson India has ever produced. A minor planet has also been named ‘(4538) Vishyanand’. His stature can be gauged by the fact that over a dozen countries have issued postal stamps featuring Anand and few are shown below:
Anand was born on 11 December 1969 and the author wishes to celebrate his 52 birthday with interesting tours of knight on 4x13 (= 52) and 11x12 (which corresponds to 11 December) board. Knight is the only piece whose move has not changed since the conception of chess before 6th century AD in India. Its weird move has always fascinated chess players. Readers may like to recall Lasker-Capablanca 1914 game where magical knight sorties by Lasker demolished mighty Capablanca. Some 100 years later, game 6 of the Anand – Topalov World Championship Match 2010 saw Anand making 13 consecutive knight moves shown in Figure 5b. Some commentators joked that Anand is solving the knight tour puzzle! ‘Tour of knight’ is over a millennium old puzzle – view AIWCF Bulletin 2021 Second Issue. The challenge is to move a knight over an empty board in such a way that it visits all the cells in successive jumps, without visiting any cell twice. Figure 1 is a semi-magic tour of knight on 4x13 board. Here sum of all the columns is 106 and the sums of rows are consecutive numbers having an aesthetic appeal.
Fig.1. Semi-magic tour of knight on 4x13 board
The incessant work of chess players as well as mathematicians has created a vast literature related to the ‘Tour of knight’ conundrum. There are zillions of knight's tours on 11x12 board and their exact number is unknown but composing knight tour with magic properties is more challenging and fascinating. Magic knight tour has all the rows and all the columns adding up to magic constant. A semi-magic tour has either all the rows or all the columns, but not both, adding up to magic constant. Figure 2 is also a semi-magic knight tour on 11x12 board. Here, all the consecutive numbers from first cell (1) to the last cell (132) are at knight's move and sum of all the rows is 798. Since it is also an ‘odd by even’ size board, all the columns can't sum up to a magic constant because their sums are even and odd, alternately.
Fig.2. Semi-magic tour of knight on 11 x 12 board
Eagle-eyed readers must have spotted that the tour shown here is an open tour of knight that is, cell 1 and cell 132 are not connected by knight move. Closed (or reentrant) knight tours are more challenging and readers are encouraged to compose such tours.
Figure 3 shows monogram tours (knight moves delineating letter shapes) with square numbers 12, 22, 32 … 112, that is 1, 4, 9 … 121 delineating letters ‘V’ and ‘A’, the first letters of his name. Readers may like to compose monogram tours delineating other letters of his name. Figure 4a has the consecutive square numbers arranged in a square formation. Figure 4b has the multiples of 11 along the central column. Here the move segments are alternately on either side of the central column up to 96. Readers are urged to improve upon it.
Fig.3. Monogram tours delineating letters ‘V’ and ‘A’
Fig.4. Figured tour with (a) square numbers in square formation (b) multiples of 11
Figure 5a is the prettiest of all. Here, the line joining the consecutive square numbers is heart shaped – the universal symbol of love. We adore, admire and love you Vishy!! Whole world is proud of you. Many happy returns of the day Vishy – as he is fondly known among chess elites – and we wish you a long and happy life ahead.
Fig.5. (a) Figured tour of knight with consecutive square numbers making ❤ shape (b) Anand's 13 consecutive knight moves – a record in any world chess championship
This article is dedicated to GM Viswanathan Anand and the author wishes to celebrate centenary of his birthday. Amen.