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A Zero-Sum Game is a puzzle in Professor Layton and the Unwound Future. The puzzle must be solved in order to progress the story.

Puzzle

US Version

For each of the four squares below, there is a way to display the numbers zero to nine. Tapping each of the four buttons, A, B, C, and D, will change the numbers according to a hidden set of rules.

Figure out the hidden rules, and set all the numbers to zero.

UK Version

For each of the four squares below, there is a way to display all the numbers from zero to nine. Touch the four buttons, A, B, C and D, to change the numbers according to a hidden set of rules.

Work out the hidden rules and set all the numbers to zero.

Hints




Click a Tab to reveal the Hint.

US Version

Notice that when a number reaches nine, it flips back to zero. In other words, the numbers are on a loop. So, push the buttons as many times as you like. It won't mess up anything.

If you restart the puzzle several times and pay close attention to what each button does, the rules should become clear.

UK Version

Notice that when a number goes over nine, the counter starts again at zero. In other words, the numbers are on a loop, so touch the buttons as many times as you like. It won't mess anything up.

If you touch each button several times and pay close attention to what each one does, the rules should become clear.

US Version

The colored rectangle connected to each button shows which two squares it affects. When a button is tapped, the two numbers within its colored rectangle increase according to a hidden rule. Study the numbers one button at a time.

UK Version

The coloured rectangle connected to each button indicates the two squares that it affects. When a button is touched, the two numbers within its coloured rectangle increase according to a hidden rule. Study what happens to the numbers when you touch each button.

Button A adds five.
Button B adds three.

US Version

The rules for buttons C and D shouldn't be hard to figure out now.

But, even knowing the rules, how do you turn all the numbers to zero?

UK Version

It shouldn't be too hard to work out the rules for buttons C and D now.

But even knowing the rules, how do you turn all the numbers to zero?

Don't get too frustrated if you're still stuck. This puzzle is tricky.

US Version

To solve it, don't tap the A button at all at first. Tap buttons C and D until the numbers in A's rectangle both read five. After that, you'll be able to solve it in no time.

UK Version

To solve it, don't touch button A at first, instead touch buttons C and D until the numbers in A's rectangle are both five. After that, you'll be able to solve it in no time.


Solution

Correct

Wonderful job!

Button A adds five, B adds three, C adds seven, and D adds four.

You must have worked that out. Unless you're one of those people that just kept pounding the buttons until they set everything to zero...

  • Initial position
  • Tap A once
  • Tap B nine times
  • Tap C seven times
  • Tap D four times

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

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