WMC 2018 Senior Problem 15

Algebra Level 2

Compute

∑ n = 1 20 ⌊ log ⁡ 2 n ⌋ \large \sum_{n=1}^{20}\left\lfloor\log_2{n}\right\rfloor

Notation: ⌊ ⋅ ⌋ \lfloor \cdot \rfloor denotes the floor function .

50 46 52 48 54

Tiger Ang by Tiger Ang , 20, Malaysia

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1 solution

X X
Oct 14, 2018

From 2 to 3: 1

From 4 to 7: 2

From 8 to 15: 3

From 16 to 20: 4

So, 1 × 2 + 2 × 4 + 3 × 8 + 4 × 5 = 54 1\times2+2\times4+3\times8+4\times5=54

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