be a quadrilateral such that the excircles 
and 
of triangles 
and 
touching their sides 
and 
respectively touch the extension of 
at the same point 
.
meets 
,
and 
.
and 
is right
such that 
has a divisor in the range 
.
and no elements of 
and 
,
is an integer.
of odd degree with real coefficients such that 
.
Y by
Scientists found a new species of bird called “N-coloured rainbow”. They also found out 3 interesting facts about the bird’s life: 1) every day, N-coloured rainbow is coloured in one of N colors.
2) every day, the color is different from yesterday (not every previous day, just yesterday).
3) there are no four days i, j, k, l in the bird’s life such that i<j<k<l with colours a, b, c, d respectively for which a=c ≠ b=d.
Find the greatest possible age (in days) of this bird as a function of N.
2) every day, the color is different from yesterday (not every previous day, just yesterday).
3) there are no four days i, j, k, l in the bird’s life such that i<j<k<l with colours a, b, c, d respectively for which a=c ≠ b=d.
Find the greatest possible age (in days) of this bird as a function of N.
