Explanation
To find the number of such pairs in the word RECOVERED, we compare the distance between any two letters in the word with their distance in the English alphabet. A pair exists if the number of letters between them in the word is equal to the number of letters between them in the alphabet. This is equivalent to checking if the absolute difference in their positions in the word equals the absolute difference in their positions in the English alphabet.
Assigning numerical positions to the letters of the word RECOVERED:
R(1), E(2), C(3), O(4), V(5), E(6), R(7), E(8), D(9)
Assigning numerical values based on the English alphabet (A=1, B=2, …):
R(18), E(5), C(3), O(15), V(22), E(5), R(18), E(5), D(4)
We identify the following four pairs:
R (position 1) and O (position 4): The difference in word positions is 4 - 1 = 3. The difference in alphabetical positions is 18 - 15 = 3. Thus, there are 2 letters between them in both cases.
R (position 1) and V (position 5): The difference in word positions is 5 - 1 = 4. The difference in alphabetical positions is 22 - 18 = 4. Thus, there are 3 letters between them in both cases.
O (position 4) and R (position 7): The difference in word positions is 7 - 4 = 3. The difference in alphabetical positions is 18 - 15 = 3. Thus, there are 2 letters between them in both cases.
E (position 8) and D (position 9): The difference in word positions is 9 - 8 = 1. The difference in alphabetical positions is 5 - 4 = 1. Thus, there are 0 letters between them in both cases as they are adjacent.