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Algebra Level 4

The fastest supercomputer Sunway TaihuLight is commissioned to generate all \(4 \times 4\) pixel, 8 bit grayscale images.

The supercomputer can generate \(10^{15}\) images per second. Assume that one day has exactly 86400 seconds, and a year has \(365.25\) days (on average). Now for each century (hundred years) that passes without the task getting complete, a single grain of rice (weighing \(\dfrac1{64}\) grams) is added to a pile of rice grains.

When the task is complete, the heap weigh \(T\) kilograms.

Find the value of \(\lfloor T \rfloor\)?

\[\] Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.


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