is given. Let 
be set of all 
segments of real line of type ![$[i, j]$](http://latex.artofproblemsolving.com/a/6/4/a644edd67caa59eaded765c417b6d9822f782ec2.png)
,
and 
are integers, 
.
is said to be valuable if the intersection of any two segments from 
is either empty, or is a segment of nonzero length belonging to 
rows of coins. There is 1 coin in the first row, 2 coins in the second row, 3 coins in the third row, and so on, up to 
satisfying 
,![\[ \frac{a^4+5b^4}{a(a+2b)} + \frac{b^4+5c^4}{b(b+2c)} + \frac{c^4+5a^4}{c(c+2a)} \geq 1- ab-bc-ca \]](http://latex.artofproblemsolving.com/f/e/8/fe85cf52b883c214806ab837a2eb25cebb511d7b.png)
Y by
Given triangle 
with 
, 
, 
. Bob and Bill in turn (BoB is the first) cut the triangle along any straight line so that two new triangles with area more than or equal to 
appear. After that an obtuse-angled triangle (or any of two right-angled triangles) is deleted and the procedure is repeated with the remained triangle. The player losses if he cannot do the next cutting. Determine, who of the players wins if both play in the best way.
with 
, 
, 
. Bob and Bill in turn (BoB is the first) cut the triangle along any straight line so that two new triangles with area more than or equal to 
appear. After that an obtuse-angled triangle (or any of two right-angled triangles) is deleted and the procedure is repeated with the remained triangle. The player losses if he cannot do the next cutting. Determine, who of the players wins if both play in the best way.This post has been edited 3 times. Last edited by parmenides51, Dec 16, 2022, 8:21 AM
