Enigma 1490: Board with squares?
20 November 2012
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From New Scientist #2652, 19th April 2008
A snakes and ladders board consists of a 10-by-10 grid of squares. In the first row (at the bottom) the squares are numbered from 1 to 10 from left to right. Then in the second row the squares are numbered 11 to 20 from right to left. Then in the third row they are 21 to 30 from left to right again, and so on, ending up at square “100” in the top left-hand corner.
From such a board I have cut out a square-shaped piece consisting precisely of some of its squares, but not including square “1”. The total of all the numbers in my piece is the square of one of the numbers in it.
What is that total?