Question

Charlie forgot the first digit of the lock combination: ...85,325. He just remembered that the entire combination was a multiple of 3.

How many checks does he needs to do to open the lock?

The missing digit in ascending order could be:

Answer 1

As you know, the number will be a multiple of 3 if the sum of digits is a multiple of 3. The digits shown add to 23, which has a remainder of 2 when divided by 3. The missing digit will be a value that makes a multiple of 3 when it is added to 2. You can use your number sense, or you can write an equation.
.. x +2 = 3n . . . . . for n = 0, 1, 2, 3, 4
.. x = 3n -2
.. x = -2, 1, 4, 7, 10 . . . . . only positive single-digits are of interest

The missing digit must be 1, 4, or 7.

Up to 3 checks must be performed.