If N² = 12345678987654321 , then how many digits does the number N have ?

The given number N² = 12345678987654321 follows a specific pattern. This pattern is observed when squaring numbers consisting only of the digit '1'.

Consider these examples: 1² = 1 (1 digit in N) 11² = 121 (2 digits in N) 111² = 12321 (3 digits in N) 1111² = 1234321 (4 digits in N)

In general, if a number N consists of 'k' ones (e.g., N = 11...1, k times), then N² will be a number that ascends from 1 to 'k' and then descends back to 1.

For N² = 12345678987654321, the digits ascend to 9 and then descend back to 1. This indicates that the number N must consist of nine '1's. So, N = 111,111,111.

Counting the digits in N = 111,111,111, we find that N has 9 digits.

Therefore, the correct option is B.

Options analysis: A) 8: Incorrect, as N has 9 digits. B) 9: Correct, as N = 111,111,111 has 9 digits. C) 10: Incorrect. D) 11: Incorrect.