How many pairs of letters are there in the word “Adequate” each of which have…

Concept: A letter-pair “matches” when the number of letters between the two letters as they appear in the word equals the number of letters between the same two letters in the A-to-Z alphabet. Every pair in the word must be tested against this rule; only pairs where both counts are equal are counted.

1. Number the letters of ADEQUATE by position: A(1) D(2) E(3) Q(4) U(5) A(6) T(7) E(8).

2. Testing D-E (positions 2 and 3): the word gap is 3 − 2 − 1 = 0. In the alphabet, D is the 4th letter and E is the 5th, so the alphabet gap is 5 − 4 − 1 = 0 (nothing between D and E). Both gaps equal 0 — D-E qualifies.

3. Testing Q-T (positions 4 and 7): the word gap is 7 − 4 − 1 = 2 (the letters U and A lie between them). In the alphabet, Q is the 17th letter and T is the 20th, so the alphabet gap is 20 − 17 − 1 = 2 (R and S lie between them). Both gaps equal 2 — Q-T qualifies.

4. Checking every other combination of letters in the word gives two different gap values on the two counts, so none of the remaining combinations qualify.

Cross-check: D-E are adjacent letters both in the word and in the alphabet, so both gaps are 0 — confirmed. Q-T have 2 letters between them in the word (U, A) and 2 letters between them in the alphabet (R, S) — confirmed. Exactly two valid pairs exist, so the answer is Two.