# Problem of the Day

Consider a set of 729 consecutive integers whose smallest element is . If the arithmetic mean of this set of numbers is 1,072, what is the value of ?

A. 672

B. 708

C. 780

D. 828

E. 1,236

### Solution

[latexpage]

The key to solving this problem is recognizing that the arithmetic mean of a set of consecutive integers is the same as its median. In other words, 1,072 is precisely in the middle of the 729 consecutive integers. The remaining 728 integers will be divided equally above and below 1,072. Half of 728 is 364, so the smallest element will be $1,072-364=708$.

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