This problem is based on decimal system conversion. In the given problem we have to convert the given number to the another number system from decimal and finding the sum of the digits later on.
What is the greatest possible sum of the digits in the base-seven representation of a positive integer less than $2019$?
$\textbf{(A) } 11 \qquad\textbf{(B) } 14 \qquad\textbf{(C) } 22 \qquad\textbf{(D) } 23 \qquad\textbf{(E) } 27$
AMC 10B, 2019 Problem 12
Decimal system conversion
6 out of 10
challenges and thrills of pre college mathematics
First of all 2019 is in base 10, see below
\(2019=2*10^3+0*10^2+1*10^1+9+10^0\).
so we have to convert it in the system having base 7.
After converting we will get
But we have to maximize the sum of digits. So we need to increase the number of 6 in the converted number(in base 7) and it is because 6 is the largest number in the number system having base 7.
The conversion of maximize 6 in the number will occur with either of the numbers $4666_7$ or $5566_7$.
and now we can simply find the sum of the digits.
I.S.I. & C.M.I. Entrance Program
Taught by students and alumni of I.S.I. & C.M.I.
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.
Cheenta students shine at the Purple Comet Math Meet 2025 organized by Titu Andreescu and Jonathan Kanewith top national and global ranks.
Celebrate the success of Cheenta students in the Stanford Math Tournament. The Unified Vectors team achieved Top 20 in the Team Round.