Commemorating 140 Years of New Zealand Chess Championship
by Awani Kumar, Lucknow, INDIA
New Zealand has a rich chess tradition and its first chess championship was organized over 140 years ago. To commemorate this glorious event, the author has composed an interesting tour of knight on 10x14 (=140) cell board.
Tour of knight is a classical puzzle, over a millennium old – almost as old as the game of chess itself. The task is to move a knight over an an empty board so that it covers all the cells in consecutive jumps, without visiting any cell twice. According to Dickins, [1] “The earliest known Knight’s Tour dates from about 900 A.D. ...” The incessant work of chess aficionados, mathematicians and people from other walks of life has created its vast literature in multitude languages over centuries. Jelliss [2] has meticulously compiled it. There are zillions of knight’s tours on 10x14 board and the exact number is unknown but tours having magic properties are rare and thus more challenging and interesting. A magic tour of knight has all the rows and all the columns sum up to a magic constant. Semi-magic tour has only the rows or columns, but not both, sum up to a magic constant. Figure 1 shows a semi-magic tour of knight on 10x14 board. Readers can see that all the consecutive numbers from 1 to 140 are at knight’s move. Moreover, sum of all the fourteen columns is 705 and six (out of ten) rows are adding up to 987. So it has 20 magic lines (out of 24). It is an open tour of knight, that is, the first (1) and the last cell (140) are not connected by knight move.
| 1 | 138 | 67 | 74 | 5 | 136 | 65 | 78 | 9 | 132 | 61 | 80 | 11 | 130 | 987 | |
| 70 | 73 | 4 | 137 | 66 | 75 | 6 | 133 | 62 | 79 | 10 | 131 | 60 | 81 | 987 | |
| 139 | 2 | 71 | 68 | 135 | 64 | 77 | 8 | 127 | 14 | 83 | 58 | 129 | 12 | 987 | |
| 72 | 69 | 140 | 3 | 76 | 7 | 134 | 63 | 84 | 57 | 128 | 13 | 82 | 59 | 987 | |
| 91 | 88 | 47 | 54 | 107 | 86 | 37 | 56 | 17 | 126 | 15 | 24 | 19 | 124 | 891 | |
| 46 | 53 | 90 | 87 | 38 | 55 | 108 | 85 | 118 | 25 | 18 | 125 | 116 | 23 | 987 | |
| 89 | 92 | 45 | 48 | 99 | 106 | 39 | 36 | 109 | 16 | 117 | 22 | 123 | 20 | 961 | |
| 52 | 49 | 96 | 93 | 42 | 35 | 102 | 105 | 26 | 119 | 122 | 113 | 30 | 115 | 1099 | |
| 95 | 44 | 51 | 98 | 103 | 100 | 33 | 40 | 121 | 110 | 31 | 28 | 21 | 112 | 987 | |
| 50 | 97 | 94 | 43 | 34 | 41 | 104 | 101 | 32 | 27 | 120 | 111 | 114 | 29 | 997 | |
| 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 | 705 |
Fig.1. Semi-magic tour of knight on 10x14 board
How many such tours are there on 10x14 board? Are there closed semi-magic tours? Can we further improve
upon it? Readers are requested to look into these questions and may like to compose more such tours.
Congratulations New Zealand Chess Federation! We wish to celebrate its bicentenary. Amen!
References
1. A. Dickins; A Guide to Fairy Chess, Dover Publications, 1971, p. 27.
2. G.P. Jelliss; Knight’s Tours Notes, available at http://www.mayhematics.com.