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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.

CVUK010S

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

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