of natural numbers such that
ones are written in a circle. Petya and Vasya take turns making 
moves each. In each move, Petya chooses 9 consecutive numbers and decreases each by 
.
consecutive numbers and increases each by 
.
be an acute-angled triangle with circumcircle 
and circumcentre 
.
and 
lie on 
and 
.
meet 
at 
,
meet 
at 
.
and 
have an intersection lie on line 
.
such that 
then find minimal value of 
Y by Funcshun840
A computer science teacher has asked his students to write a program that, given a list of 
numbers 
, calculates the list 
where 
is the number of times the number 
appears in the list. So, for example, for the list 
, the program returns the list 
.
Next, the teacher asked Alexandre to run the program for a list of
numbers. Then he asked him to apply the program to the resulting list, and so on, until a number greater than or equal to 
appears in the list. Find the largest value of for which, whatever the initial list of positive integers 
, it is possible for Alexander to do what the teacher asked him to do.
numbers 
, calculates the list 
where 
is the number of times the number 
appears in the list. So, for example, for the list 
, the program returns the list 
.Next, the teacher asked Alexandre to run the program for a list of
numbers. Then he asked him to apply the program to the resulting list, and so on, until a number greater than or equal to 
appears in the list. Find the largest value of for which, whatever the initial list of positive integers 
, it is possible for Alexander to do what the teacher asked him to do.
