5.X.2. COUNTING RECTANGLES OR SQUARES
I have just seen M. Adams. There are probably earlier examples of these types of problems.
Anon. Prob. 63. Hobbies 30 (No. 778) (10 Sep 1910) 488 & 31 (No. 781) (1 Oct 1910) 2. How many rectangles on a 4 x 4 chessboard? Solution says 100, which is correct, but then says they are of 17 different types -- I can only get 16 types.
Blyth. Match-Stick Magic. 1921. Counting the squares, p. 47. Count the squares on a 4 x 4 chessboard made of matches with an extra unit square around the central point. The extra unit square gives 5 additional squares beyond the usual 1 + 4 + 9 + 16.
King. Best 100. 1927. No. 9, pp. 10 & 40. = Foulsham's, no. 5, pp. 6 & 10. 4 x 4 board with some diagonals yielding one extra square.
Loyd Jr. SLAHP. 1928. How many rectangles?, pp. 80 & 117. Asks for the number of squares and rectangles on a 4 x 4 board (i.e. a 5 x 5 lattice of points). Says answers are 1 + 4 + 9 + 16 and (1 + 2 + 3 + 4)2 and that these generalise to any size of board.
Dostları ilə paylaş: |
