Directions: Find the number of letter pairs in the given word.

How many such pairs of letters are there in the word ‘POPULATION’, each of which has as many letters between them in the word as they have in the English alphabet (both in forward and backward directions)?

The correct option is More than three.

To find the number of letter pairs in the word ‘POPULATION’ that have as many letters between them in the word as in the English alphabet (in both forward and backward directions), let us write down each letter along with its positional number in the English alphabet:

1. P = 16
2. O = 15
3. P = 16
4. U = 21
5. L = 12
6. A = 1
7. T = 20
8. I = 9
9. O = 15
10. N = 14

Now, let us examine the pairs of letters and compare their positions in the word against their distance in the alphabet:

1. Pair (P at position 1 and O at position 2):
Distance in the word = 1
Distance in the English alphabet (O to P) = 1
This forms a valid pair.

2. Pair (O at position 2 and P at position 3):
Distance in the word = 1
Distance in the English alphabet (O to P) = 1
This forms a valid pair.

3. Pair (O at position 2 and L at position 5):
Distance in the word =
$5-2=3$
Distance in the English alphabet =
$15-12=3$
(letters between L and O: M, N)
This forms a valid pair.

4. Pair (P at position 3 and T at position 7):
Distance in the word =
$7-3=4$
Distance in the English alphabet =
$20-16=4$
(letters between P and T: Q, R, S)
This forms a valid pair.

5. Pair (O at position 2 and T at position 7):
Distance in the word =
$7-2=5$
Distance in the English alphabet =
$20-15=5$
(letters between O and T: P, Q, R, S)
This forms a valid pair.

6. Pair (O at position 9 and N at position 10):
Distance in the word = 1
Distance in the English alphabet (N to O) = 1
This forms a valid pair.

Since we have found at least 6 valid pairs of letters, the total number of pairs is clearly More than three.