Sources page biographical material

6.T. NO THREE IN A LINE PROBLEM
See also section 6.AO.2.
Loyd. Problem 14: A crow puzzle. Tit Bits 31 (16 Jan & 6 Feb 1897) 287 & 343. = Cyclopedia, 1914, Crows in the corn, pp. 110 & 353. = MPSL1, prob. 114, pp. 113 & 163 164. 8 queens with no two attacking and no three in any line.

Dudeney. The Tribune (7 Nov 1906) 1. ??NX. = AM, prob. 317, pp. 94 & 222. Asks for a solution with two men in the centre 2 x 2 square.

Loyd. Sam Loyd's Puzzle Magazine, January 1908. ??NYS. (Given in A. C. White; Sam Loyd and His Chess Problems; 1913, op. cit. in 1; p. 100, where it is described as the only solution with 2 pieces in the 4 central squares.)

Ahrens, MUS I 227, 1910, says he first had this in a letter from E. B. Escott dated 1 Apr 1909. (W. Moser, below, refers this to the 1st ed., 1900, but this must be due to his not having seen it.)

C. H. Bullivant. Home Fun, 1910, op. cit. in 5.S. Part VI, Chap. IV: No. 2: Another draught puzzle, pp. 515 & 520. The problem says "no three men shall be in a line, either horizontally or perpendicularly". The solution says "no three are in a line in any direction" and the diagram shows this is indeed true.

Loyd. Picket posts. Cyclopedia, 1914, pp. 105 & 352. = MPSL2, prob. 48, pp. 34 & 136. 2 pieces initially placed in the 4 central squares.

Blyth. Match-Stick Magic. 1921. Matchstick board game, p. 73. 6 x 6 version phrased as putting "only two in any one line: horizontal, perpendicular, or diagonal." However, his symmetric solution has three in a row on lines of slope 2.

King. Best 100. 1927. No. 69, pp. 28 & 55. Problem on the 6 x 6 board -- gives a symmetric solution. Says "there are two coins on every row" including "diagonally across it", but he has three in a row on lines of slope 2.

Loyd Jr. SLAHP. 1928. Checkers in rows, pp. 40 & 98. Different solution than in Cyclopedia.

M. Adams. Puzzle Book. 1939. Prob. C.83: Stars in their courses, pp. 144 & 181. Same solution as King, but he says "two stars in each vertical row, two in each horizontal row, and two in each of the the two diagonals .... There must not be more than two stars in the same straight line", but he has three in a row on lines of slope 2.

W. O. J. Moser & J. Pach. No three in line problem. In: 100 Research Problems in Discrete Geometry 1986; McGill Univ., 1986. Problem 23, pp. 23.1 -- 23.4. Survey with 25 references. Solutions are known on the n x n board for n  16 and for even n  26. Solutions with the symmetries of the square are only known for n = 2, 4, 10.