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Massive Gemstones It All Adds Up Black and White Balls

It All Adds Up is a weekly puzzle in Professor Layton and the Unwound Future.

Puzzle[]

Aside from 28 itself, the number 28 is divisible by 1, 2, 4, 7, and 14.

When you add these numbers together, you get 1 + 2 + 4 + 7 + 14 = 28. Neat, huh! They add up to the original number.

Now for the puzzle part:

What is the smallest number for which the sum of its divisors (not including the number itself) equals the original number?

Hints[]

Click a Tab to reveal the Hint.

The answer is a single-digit number.


Solution[]

Incorrect[]

Too bad!

Don't be intimidated by the fact that this is a calculation problem. Just think about it for a bit. It's easier than you might expect at first.

Correct[]

Nice work!

The answer is 6.

The number 6 is divisible by 1, 2, 3, and 6, so if you don't include 6 in the sum, you get 1 + 2+ 3 = 6!

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A big thanks to http://professorlayton3walkthrough.blogspot.com