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No calc please.

 May 28, 2019
 #1
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\(8=2^3.\)

 

Thus, we have \(\left \lfloor \frac{100}{2} \right \rfloor+\left \lfloor \frac{100}{4} \right \rfloor+...+\left \lfloor \frac{100}{32} \right \rfloor+\left \lfloor \frac{100}{64} \right \rfloor=97\). Since \(97=32*3+1\)\(\boxed{32}\) is our searched answer.

 

-azsun

 May 28, 2019

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