Enigma 1225: Rows are columns
16 June 2015
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From New Scientist #2381, 8th February 2003 [link]
First draw a chessboard. Now number the horizontal rows 1, 2, …, 8 from top to bottom and number the vertical columns 1, 2, …, 8 from left to right. You have to put a whole number in each of the sixty-four squares, subject to the following:
1. No two rows are exactly the same.
2. Each row is equal to one of the columns, but not to the column with the same number as the row.
3. If N is the largest number you write on the chessboard then you must also write 1, 2, …, N−1 on the chessboard.
The sum of the sixty-four numbers you write on the chessboard is called your total.
What is the largest total you can obtain?
See also Enigma 1248.