of positive integers such that
be a circle inscribed inside a rhombus 
.
and 
be variable points on 
and 
respectively, such as 
is always the tangent line to 
is the same.
,
such that any graph with 
vertices and at least 
regions of a three-set Venn Diagram with 
colors such that each color is used at least once? Two colorings are considered the same if one can be reached from the other by rotation and reflection.
satisfy that 
.
and 
Prove that
Let 
Prove that
of them have the same color. I want to reshuffle the cupcakes such that each plate is replaced by a different color cupcake. Determine how many ways to reshuffle when:
.
.
is called beautiful if the are at least 
integers 
such that in base 
we have that 
end in the same digit. Find the sum of the two smallest beautiful numbers.
be the Fibonacci numbers, defined by 
and 
.
,
satisfying 
Prove that 
Proposed by Phan Ngoc Chau
and 
. 
where 
are primes, show that 
can never be a perfect square.
Y by
In a 
Domino game, each tile is square and divided into four spaces, as shown in the figure. In each box there is a number of points that varies from 
points (empty) to 
points. Two Domino tiles are equal if it is possible to rotate one of the two tiles until the other is obtained. In a Domino pack, what is the maximum number of different tiles that can be such that on each tile at least two squares have the same number of points?
Domino game, each tile is square and divided into four spaces, as shown in the figure. In each box there is a number of points that varies from 
points (empty) to 
points. Two Domino tiles are equal if it is possible to rotate one of the two tiles until the other is obtained. In a Domino pack, what is the maximum number of different tiles that can be such that on each tile at least two squares have the same number of points?This post has been edited 1 time. Last edited by parmenides51, Mar 26, 2024, 5:25 AM
