I am carrot +_+
There are \(286\) carrots of \(143\) different shades such that there are exactly \(2\) carrots of each shade. All of these carrots after treating with the machine, are filled in a bag.
There are \(11^n\) different compositions possible for this bag. Find \(n\).
Details and Assumptions:-
\(\bullet\) The carrots formed by multiplying one particular carrot are identical (due to magic of the multiplier).
\(\bullet\) The \(143\) different shades are well distinguishable, no 2 look alike.
This problem is a part of the set Vegetable Combinatorics