[CV010] Four Digits

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009 - One Poor Pooch

010 - Four Digits

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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

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.

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