[/quote]
,
then prove
.
?
be a positive integer. A Japanese triangle consists of 
circles arranged in an equilateral triangular shape such that for each 
,
,
,
row contains exactly 
circles, exactly one of which is coloured red. A ninja path in a Japanese triangle is a sequence of 
,
such that in each Japanese triangle there is a ninja path containing at least 
,
and 
.
is prime, 
with 
and 
be a function such that for every regular 
-
we have 
.
for all reals 
.
be a triangle 
)
are the altitudes of the triangle. The bisector of 
intersects 
at 
.
be a point such that 
and 
.
passes through the midpoint of 
.
.
with 
and at most one of them being zero, show that![\[\frac{1}{\max(a^2,b)}+\frac{1}{\max(b^2,c)}+\frac{1}{\max(c^2,a)}\geq\frac{27}{4}\]](http://latex.artofproblemsolving.com/9/e/1/9e14a9ef2d1a0a98006bcf716fa33c3d9ea29bd5.png)
Y by
A squadron of 
ships is located on a 
square checkered field. Each ships lies on a 
rectangle with sides along the grid lines (no two ships share the same rectangle).
a) Prove that you can fire
shots so that sure to get into some ship.
b) Is it possible to get by with
shots?
ships is located on a 
square checkered field. Each ships lies on a 
rectangle with sides along the grid lines (no two ships share the same rectangle).a) Prove that you can fire
shots so that sure to get into some ship.b) Is it possible to get by with
shots?This post has been edited 2 times. Last edited by parmenides51, Jun 19, 2021, 5:36 PM
