Find the Missing Digit in 632▯: Divisible by 3 Challenge

To solve this problem, we'll follow these steps:

• Step 1: Calculate the sum of the known digits $6 + 3 + 2 = 11$.

• Step 2: Consider each choice for the missing digit and calculate the new sum:

  • $▯ = 9 : \quad 11 + 9 = 20$ (not divisible by 3)

  • $▯=8:\quad11+8=19$ (not divisible by 3)

  • $▯=7:\quad11+7=18$ (divisible by 3)

  • $▯=5:\quad11+5=16$ (not divisible by 3)

Check which sum is divisible by 3. The sum of 18 (when ▯ is replaced by 7) is divisible by 3.

Hence, the choice $\boxed{7}$ completes the number so it is divisible by 3 without a remainder.

Therefore, the correct digit to complete the number is $7$.