15

Part of 2016 LMT

Problems(2)

2016 LMT Individual #15

Source:

For nonnegative integers

n

f(n)

be the number of digits of

n

that are at least

5

g(n)=3^{f(n)}

\sum_{i=1}^{1000} g(i).

Proposed by Nathan Ramesh

2016 LMT Theme #15

Source:

A round robin tournament is held with

2016

participants. Each player plays each other player once and exactly one game results in a tie. Let

W

be the sum of the squares of each team's win total and let

L

be the sum of the squares of each team's loss total. Find the maximum possible value of

W-L

.
Proposed by Matthew Weiss