Let k≥1 be a positive integer.We consider 4k chips, 2k of which are red and 2k of which are blue. A sequence of those 4k chips can be transformed into another sequence by a so-called move, consisting of interchanging a number (possibly one) of consecutive red chips with an
equal number of consecutive blue chips. For example, we can move from rbbbrrrb to rrrbrbbb where r denotes a red chip and b denotes a blue chip.Determine the smallest number n (as a function of k) such that starting from any initial sequence of the 4k chips, we need at most n moves to reach the state in which the first 2k chips are red. functionceiling functionalgorithmcombinatorics unsolvedcombinatorics