Question

find the rank of the word 'rejuvenescence' ?

Answer 1

41525947

Answer 2

The rank of a word is found by summing the number of permutations of letters lexicographically smaller than the given word at each position, plus one. For a word with repeated letters, the number of permutations is calculated using the formula $N! / (n_1! n_2! ... n_k!)$.

1. Count letter frequencies: R(1), E(4), J(1), U(1), V(1), N(2), S(2), C(1) for 'rejuvenescence' (13 letters).
2. For each letter in the target word, count how many permutations exist starting with a lexicographically smaller letter from the available set.
3. Subtract the chosen letter from the available set and repeat for the next position.
4. Sum all calculated permutations and add 1 for the rank of the word itself.