Unit 2 · Number Theory
Half Rounds to 50 — Max Digit Sum?
Lesson 14 of 18
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About this lesson
Work backwards: ■ is even, so ■÷2 is a whole number. That whole number rounds to 50, meaning it’s somewhere between 45 and 54. List every possible ■, compute each digit sum, and find the largest.
Chapters
0:00Introduction
0:21The Question
1:03Uncovering the Rounding Boundaries
1:34Solving for the Boundaries of the Hidden Number
2:04Optimising for the Largest Digit Sum
2:43Exam Strategy — The Upper Bound Digit Trap
3:25Confirming the Final Option
Question
Elias thinks of an even number.
■ represents his number.
When he divides ■ by 2 and then rounds the result to the nearest 10, he gets 50.
▲ is the sum of the digits of ■.
What is the largest possible value of ▲?
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