Chung Kevin's favorite - (2)
Number Theory
Level
1
\[\begin{array} (26 & = & 5+6+7+8 \\ 27 & = & 8+9+10 \\ 28 & = & 1+2+3+4+5+6+7 \\ 29 & = & 14+15 \\ 30 & = & 4+5+6+7+8 \\ 31 & = & 15+16 \end{array}\]
If you see the above numbers , they can be represented as a sum of some consecutive numbers.If 32 can be expressed as \(\displaystyle\sum_{i=1}^n a_i\) , where \(a_1,a_2,a_3, \dots a_n\) are some consecutive positive numbers , compute \(\displaystyle\prod_{i=1}^n a_i\).
Note: If you think that 32 is not lucky enough to have such representation , input the answer as 999.
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by
Nihar Mahajan