[DB120] Tug of War

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119 - The Fake Coins

120 - Tug of War

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Tug of War is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

Teams of horses are participating in tug-of-war matches. All teams are drawn from an eight-horse stable.

The first three matches end in a draw. If you want the fourth match to result in a draw as well, which horses should be on the team pulling against E and F? Tap your picks.

Here are the previous matches that ended in draws:
Match 1: A B C D vs. E F G H
Match 2: H C B vs. G A
Match 3: D A vs. F H E

UK Version

Teams of horses are participating in tug-of-war matches. All teams are drawn from an eight-horse stable. The first three matches end in draws as shown:

Match 1: A B C D vs. E F G H
Match 2: H C B vs. G A
Match 3: D A vs. F H E

If you want the fourth match to result in a draw as well, which horses should be on the team pulling against E and F?

Touch a horse to add it to the team.

Hints

Click a Tab to reveal the Hint.

There's no need to do any complicated calculations. The same horses compete several times, and since a tie means the teams are equal, think about what might happen with different matchups.

US Version

You can think about the results of the first and third matches in the following way:
A B C D = E F G H
D A = F H E

If you make some substitutions, you come up with the following:
B C = G

UK Version

You can think about the results of the first and third matches in the following way:

A B C D = E F G H
D A = F H E

Subtract the bottom equation from the top equation and you can come up with the following:

B C = G

US Version

Take the information from Hint Two and the results of the second match together to infer the following:
H C B = G A
B C = G

Making a substitution, we get:
H = A

Use this to make a new team.

UK Version

Take the information from Hint 2 and the results of the second match together to infer the following:

H C B = G A
B C = G

Subtracting one from the other gives:

H = A

Use this to make a new team.

Solution

Incorrect

Too bad!

Use the results of the earlier matches to find the correct team.

Correct

US Version

Way to go!

Of course, other matchups might work, but the only one you can confirm will end in a tie based on this information is horse D.

UK Version

Well done!

Of course, other match-ups might work, but the only one you can be sure will end in a tie based on this information is horse D.

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