To solve the problem, we use the divisibility rule for 9: any number is congruent to the sum of its digits modulo 9.

Step 1: Key Observation

For a 4-digit number (X), let (S) be the sum of its digits. Then (N = X - S) is divisible by 9 (since (X \equiv S \mod 9), so (X - S \equiv 0 \mod 9)).

Step 2: Sum of Visible Digits

The visible digits of (N) are 6, 3, 7. Their sum is (6 + 3 + 7 = 16). Let the hidden digit be (d).

Since (N) is divisible by 9, the sum of all its digits (visible + hidden) must be a multiple of 9.

Step 3: Find (d)

The smallest multiple of 9 greater than 16 is 18. Thus:
(16 + d = 18 \implies d = 2).

Answer: 2

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