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In a stack of coins, each row has exactly one coin less than the row below. If we have nine coins, two such towers are possible. Of these, the tower on the left is the tallest. If you have $$2015$$ coins, the height of the tallest tower is
Correct Answer: 62
If the top row has $$m+1$$ coins and the bottom row has $$n$$ coins, the number of coins is $$\frac{n(n+1)-m(m+1)}{2}=2015$$. Hence $$\left(n-m\right)\left(n+m+1\right)=4030$$. The largest feasible value is $$n-m=62$$, obtained with $$n=63$$ and $$m=1$$, so the tallest tower has $$62$$ rows.
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