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Question 9

A 'stair-step' figure is made of alternating black and white squares in each row. All rows begin and end with white square. First four figures of the stair-step figure are shown below. Fig-1 has 1 white square, Fig-2 has 3 white and 1 black squares, Fig-3 has 6 white and 3 black squares, and it continues. What is the total number of white squares in the Fig-20?

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The white squares in successive figures are $$1, 3, 6, 10, \ldots$$, which are the triangular numbers, so Fig-$$n$$ has $$\frac{n(n + 1)}{2}$$ white squares. For $$n = 20$$ this gives $$\frac{20 \times 21}{2} = 210$$.

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