[/quote]
,
,
such that 
is a perfect square? (Here 
denotes the integer part of the real number 
?
satisfying
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2^a + 3^b + 5^c = n!
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of injective functions from the set of real numbers to itself satisfying
and 
.
is injective if 
for any distinct real numbers 
and 
.
,
such that any graph with 
{
}
distinct positive integers is 
if for every 
the number 
is divisible by the product of all numbers in 
.
positive integers.
with 
and 
.
?
is a cyclic quadrilateral inscribed in a circle of radius one unit. If 
,
be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
,
?
.
and 
externally on the sides 
and 
respectively.
meets 
at 
,
meets 
at 
and 
denotes circumcenter of 
and 
meets again on 
.
Y by VicKmath7, Adventure10
The chess piece sick rook can move along rows and columns as a regular rook, but at most by 
fields. We can place sick rooks on a square board in such a way that no two of them attack each other and no field is attacked by more than one sick rook.
a) Prove that on
board, we cannot place more than 
sick rooks.
b) Find the maximum number of sick rooks which can be placed on
board.
c) Prove that on
board, we cannot place more than 
sick rooks.
fields. We can place sick rooks on a square board in such a way that no two of them attack each other and no field is attacked by more than one sick rook.a) Prove that on
board, we cannot place more than 
sick rooks.b) Find the maximum number of sick rooks which can be placed on
board.c) Prove that on
board, we cannot place more than 
sick rooks.This post has been edited 1 time. Last edited by parmenides51, Jan 20, 2020, 5:24 PM
