How many pairs of letters are there in the word ‘CREATIVE’ which have as many letters between them in the word as in the alphabet?
1
2
3
4
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2019
C(1, 3), R(2, 18), E(3, 5), A(4, 1), T(5, 20), I(6, 9), V(7, 22), E(8, 5)
– A pair of letters (L1, L2) at word positions P1 and P2 forms a matching pair if the number of letters between them in the word, which is |P1 – P2| – 1, is equal to the number of letters between them in the alphabet, which is |AlphaPos(L1) – AlphaPos(L2)| – 1. This simplifies to checking if |P1 – P2| = |AlphaPos(L1) – AlphaPos(L2)|.
– Let’s check all pairs:
– C(1,3) with E(3,5): |1-3|=2, |3-5|=2. Match! (C-E)
– C(1,3) with E(8,5): |1-8|=7, |3-5|=2. No.
– E(3,5) with A(4,1): |3-4|=1, |5-1|=4. No.
– E(3,5) with I(6,9): |3-6|=3, |5-9|=4. No.
– E(3,5) with V(7,22): |3-7|=4, |5-22|=17. No.
– E(3,5) with E(8,5): |3-8|=5, |5-5|=0. No.
– A(4,1) with E(8,5): |4-8|=4, |1-5|=4. Match! (A-E)
– T(5,20) with V(7,22): |5-7|=2, |20-22|=2. Match! (T-V)
– Other pairs do not satisfy the condition. (Checked systematically in thought process).
– The three pairs are C-E (occurring forward from C to the first E), A-E (occurring forward from A to the second E), and T-V (occurring forward from T to V). The order in the alphabet doesn’t matter (|difference| is used).
– Note that C-E (positions 1 and 3 in word) have 1 letter (R) between them. In the alphabet, C and E have 1 letter (D) between them.
– A-E (positions 4 and 8 in word) have 3 letters (T, I, V) between them. In the alphabet, A and E have 3 letters (B, C, D) between them.
– T-V (positions 5 and 7 in word) have 1 letter (I) between them. In the alphabet, T and V have 1 letter (U) between them.