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Four Digits is a puzzle in the European version of Professor Layton and the Curious Village. For the puzzle in the American version of the game, go here.

## Puzzle

A,B, C and D are single-digit numbers. The following equations can all be made with these numbers.

A + C = D
A x B = C
C - B = B
A x 4 = D

Find the vlaues of each digit and input your answer as a four digit-number, ABCD.

## Hints

Click a Tab to reveal the Hint.

Two of the equations have D as their answer.

Your starting point should be to compare these two equations.

A + C and A x 4 both equal D.
Since A x 4 is the same as A + A + A + A, C must equal A x 3.

C - B = B. This means that C = 2 x B.

You also know from the second hint that C = 3 x A.

Only one single-digit number is divisible by both 2 and 3. Find it and you've found the key to solving the puzzle.

## Solution

### Incorrect

Too bad! Pay close attention to the equations and the answer will become clear.

### Correct

That's right! ABCD = 2368.

Since A + C and A x 4 both equal D, then C must equal A x 3. If C - B = B, then C must also equal B x 2. The only single-digit number divisible by both 2 and 3 is 6. Once you know that C = 6, the rest is easy.

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

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