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6.AO.2. PLACE AN EVEN NUMBER ON EACH LINE
See also section 6.T.

Sometimes the diagonals are considered, but it is not always clear what is intended.

Leske. Illustriertes Spielbuch für Mädchen. 1864?

Prob. 564-31, pp. 254 & 396. From a 6 x 6 array, remove 6 to leave an even number in each row. (The German 'Reihe' can be interpreted as row or column or both.) If we consider this in the first quadrant with coordinates going from 1 to 6, the removed points are: (1,2), (1,3), (2,1), (2,2), (6,1), (6,3). The use of the sixth column is peculiar and has the effect of making both diagonals odd, while the more usual use of the third column would make both diagonals even.

Prob. 583-5, pp. 285 & 403: Von folgenden 36 Punkten sechs zu streichen. As above, but each file ('Zeile') in 'all four directions' has four or six points. Deletes: (1,1), (1,2), (2,2), (2,3), (6,1), (6,3) which makes one diagonal even and one odd.

Mittenzwey. 1880. Prob. 154, pp. 31 & 83; 1895?: 177, pp. 36 & 85; 1917: 177, pp. 33 & 82. Given a 4 x 4 array, remove 6 to leave an even number in each row and column. Solution removes a 2 x 3 rectangle from a corner. [This fails -- it leaves two rows and a diagonal with an odd number. One can use the idea mentioned for Leske 564-31 to get a solution with both diagonals also being even.]

Hoffmann. 1893. Chap. VI, pp. 271-272 & 285 = Hoffmann-Hordern, pp. 186-187.

No. 22: The thirty six puzzle. Place 30 counters on a 6 x 6 board so each horizontal and each vertical line has an even number. Solution places the six blanks in a 3 x 3 corner in the obvious way. This also makes the diagonals have even numbers.

No. 23: The "Five to Four" puzzle. Place 20 counters on a 5 x 5 board subject to the above conditions. Solution puts blanks on the diagonal. This also makes the diagonals have even number.

Dudeney. The puzzle realm. Cassell's Magazine ?? (May 1908) 713-716. The crack shots. 10 pieces in a 4 x 4 array making the maximal number of even lines -- counting diagonals and short diagonals -- with an additional complication that pieces are hanging on vertical strings. The picture is used in AM, prob. 270.

Loyd. Cyclopedia. 1914. The jolly friar's puzzle, pp. 307 & 380. (= MPSL2, no. 155, pp. 109 & 172. = SLAHP: A shifty little problem, pp. 64 & 110.) 10 men on a 4 x 4 board -- make a maximal number of even rows, including diagonals and short diagonals. This is a simplification of Dudeney, 1908.

King. Best 100. 1927. No. 72, pp. 29 & 56. As in Hoffmann's No. 22, but specifically asks for even diagonals as well.

The Bile Beans Puzzle Book. 1933. No. 19: Thirty-six coins. As in Hoffmann's No. 22, but specifically asks for even diagonals as well.

Rudin. 1936. No. 151, pp. 53-54 & 111. Place 12 counters on a 6 x 6 board with two in each 'row, column and diagonal'. Reading the positions in each row, the solution is: 16, 34, 25, 25, 34, 16. Some of the short diagonals and some of the broken diagonals are empty, so he presumably isn't including these, or he meant to ask for each of these to have an even number of at most two.

M. Adams. Puzzle Book. 1939. Prob. C.179: Even stars, pp. 169 & 193. Same as Loyd.

Doubleday - 1. 1969. Prob. 61: Milky Way, pp. 76 & 167. = Doubleday - 5, pp. 85-86. 6 x 6 array with two opposite corners already filled. Add ten more counters so that no row, column or diagonal has more than two counters in it. Reading the positions in each row, the solution is: 13, 35, 12, 67, 24, 46. Some short diagonals are empty or have one counter and some broken diagonals have one or four counters, so he seems to be ignoring them. Hence this is the same problem as Rudin, but with a less satisfactory solution.

Obermair. Op. cit. in 5.Z.1. 1984. Prob. 37, pp. 38 & 68. 52 men on an 8 x 8 board with all rows, columns and diagonals (both long and short) having an even number.