Finding Letter Pairs in the word PARCEL

The purpose of this question is to identify the pairs of letters in the word 'PARCEL' that have the same number of letters between them as there are in the English alphabet.

Alphabet and Word Positions

The alphabet position (A=1) and their position (index) in the word 'PARCEL' are given below:

• P: Alphabet=16, Word=0
• A: Alphabet=1, Word=1
• R: Alphabet=18, Word=2
• C: Alphabet=3, Word=3
• E: Alphabet=5, Word=4
• L: Alphabet=12, Word=5

Condition for Equal Letter Difference

A pair $(X, Y)$ is valid if the number of letters between them is the same in the word and in the alphabet. Mathematically, this occurs when the absolute difference between the alphabet positions is equal to the absolute difference between the word positions:

$ | \text{Alphabet Position}(X) - \text{Alphabet Position}(Y) | = | \text{Word Position}(X) - \text{Word Position}(Y) | $

Counting Valid Pairs

Let's check the possible pairs using this condition:

1. Pair (P, R):
   • Alphabet Difference: $|16 - 18| = 2$
   • Word Difference: $|0 - 2| = 2$
   • Result: Matches.
2. Pair (A, C):
   • Alphabet Difference: $|1 - 3| = 2$
   • Word Difference: $|1 - 3| = 2$
   • Result: Matches.

For all other possible pairs (like P and A, P and C, A and R, etc.), the differences in positions in the alphabet and the word are not the same, so they are not valid pairs.

Final Answer

There are a total of two such pairs in the word 'PARCEL' (P, R and A, C) that have the same number of letters between them as they do in the English alphabet.