On a certain island, every two people are either friends or foes, the king wants to hold a certain competition in which out of the 6 competitors 3 people are chosen (randomly) every round to perform a certain task, but the king's condition is that in every team of 3 there will not be 3 friends or 3 foes, find the king a group of 6 people for this competition...

sorry anza, but i dint get what we have to do in the question

yep! kudos

cool buddy, well done that replacement of x by z was very well thought

That's what intuition may tell you, but not true. Try it with sqrt(2).

sqrt(2) = 1.414214

sqrt(2)^sqrt(2) = 1.632527

sqrt(2)^ 1.632527 = 1.76084

sqrt(2)^1.76084 = 1.840911

keep going and it converges on 2.

However sqrt(2) isn't quite the limit, you can go higher yet. (But not so high as sqrt(e) which was k-man's last guess)

sqrt(e) = e^(1/2) is too high, it doesn't work. You're getting warmer though

y = x^(x^(x^(...

ln(y) = x^(x^(x..)))))..) * ln(x) = y * ln(x)

so we have

ln(y) = y*ln(x)

now take the derivative with respect to x:

(dy/dx) / y = (dy/dx)*ln(x) + y/x

from here it's just algebra:

-y/x = (dy/dx) * (ln(x) - 1/y)

(dy/dx) = -y / ( x*(ln(x) - 1/y) )

f ' (x) = -f(x) / (xlnx - x/f(x))

which is the same as:

f ' (x) = f(x)^2 / (x - x*ln(x)*f(x) )

ya i got f'(x) by doing it implicitly but like k-man, my intuition tells me sqrt(2) might work and tend to be finite, are u sure about d answer?