[/quote]
,
be a positive integer. There are two numbers written on a blackboard, one red and one blue. Initially, both are 0. We define the following procedure: at each step, we choose a nonnegative integer 
(not necessarily distinct from the previously chosen ones), and, if the red and blue numbers are 
and 
respectively, we replace them with 
and 
,
.
are positiv real number, such that 
prove inequality 
and 
.
be the set of all positive integers. Determine all subsets 
of 
such that
and 
intersect at 
be the circumcircle of the triangle 
;
and 
intersects 
.
on 
.
and 
meet at 
,
.
.
?
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 
,
,
and 
.
is prime, 
with 
and 
Y by Adventure10, Mango247
Let's take a 
rectangle of paper; the side 
measures 
cm and the side 
measures 
cm.
We do three folds:
1.We take the side on the side and call 
the point on the side that coincides with 
.
A right trapezoid
is then formed.
2. We fold so that
and 
coincide. A -sided polygon 
is formed.
3. We fold again by matching
with 
and with . A new right trapezoid 
.
After making these folds, we make a cut perpendicular to
by its midpoint 
, obtaining the right trapezoid 
.
Calculate the area of the figure that appears as we unfold the last trapezoid.
rectangle of paper; the side 
measures 
cm and the side 
measures 
cm.We do three folds:
1.We take the
side on the side and call 
the point on the side that coincides with 
.A right trapezoid
is then formed.2. We fold so that
and 
coincide. A -sided polygon 
is formed.3. We fold again by matching
with 
and with . A new right trapezoid 
.After making these folds, we make a cut perpendicular to
by its midpoint 
, obtaining the right trapezoid 
.Calculate the area of the figure that appears as we unfold the last trapezoid
.This post has been edited 1 time. Last edited by parmenides51, Sep 14, 2018, 8:47 PM
Reason: level edit
Reason: level edit
