Sums of Sums of Sums of

Algebra Level 5

Let N=a1=12014a2=1a1a2014=1a20132014 sums1N=\underbrace{\displaystyle\sum^{2014}_{a_1=1}\sum^{a_1}_{a_2=1}\cdots \sum^{a_{2013}}_{a_{2014}=1}}_{2014\text{ sums}}1

How many zeroes to the right of the right-most non-zero decimal digit are in NN?

Details and Assumptions\text{Details and Assumptions}

  • If N=10080000N=10080000, then the answer would be 44.
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