be an acute triangle with circumcenter 
.
,
on side 
.
passing through 
at point 
.
and 
be a triangle and 
points in the same plane such that 
,
,
.
is parallel to 
,
is the midpoint of segment 
,
and
meaning 
is the least common multiple of the numbers 
.
such that
for every positive integer 
such that 
for any relatively prime natural numbers 
.
Y by Leo.Euler
At an informatics competition each student earns a score in 
on each of six problems, and their total score is the sum of the six scores (out of 
). Given two students 
and 
, we write 
if there are at least five problems on which scored strictly higher than .
Compute the smallest integer
such that the following statement is true: for every integer 
, given students 
, \dots, 
satisfying 
, the total score of is always at most points more than the total score of .
Jiahe Liu
on each of six problems, and their total score is the sum of the six scores (out of 
). Given two students 
and 
, we write 
if there are at least five problems on which scored strictly higher than .Compute the smallest integer
such that the following statement is true: for every integer 
, given students 
, \dots, 
satisfying 
, the total score of is always at most points more than the total score of .Jiahe Liu
This post has been edited 1 time. Last edited by YaoAOPS, Jan 22, 2025, 2:10 AM
is obviously the max, and is obtainable starting from 
and can increment it by a maximum of 
.
moves until we arrive at a net increase of 
,
.
.
,
.
