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MathNet 2022-part-03 — 197 problems (EN–VI) Question 56

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 56

Maddalena writes on a sheet of paper all the powers of $2$ from $1$ to $2^{100}$ (both included). How many of the numbers she wrote begin with $1$?

(A) 28 or fewer
(B) 29
(C) 30
(D) 31
(E) 32 or more.