Question 1

The central square of a $$9 \times 9$$ chessboard is white. How many white squares are there on the board? (The squares of the chessboard are coloured alternately black and white.)

Correct Answer: 41

Solution

The centre is in row 5, column 5, and moving four squares left and then four squares up preserves the colour, so the top-left corner is also white. Rows $$1, 3, 5, 7, 9$$ therefore contain 5 white squares each, while rows $$2, 4, 6, 8$$ contain 4 each. Hence the total is $$5 \times 5 + 4 \times 4 = 41$$.

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