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Floating Cottages (Rainbow Cottages in the UK version) is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

The seven floating cottages shown below are connected by 12 small bridges, which has made this little retirement community quite the tourist attraction.

A visiting couple has decided to paddle a boat out to one of the cottages and walk back to the mainland by crossing each bridge only once.

Which cottage should they start at?

UK Version

The Rainbow Cottages are very popular with the tourists, and one of the main attractions is the pleasant waterside stroll connected by 12 bridges.

A visiting couple have decided to paddle a boat out to one of the cottages and walk back to the mainland, crossing each of the twelve bridges only once.

Which cottage should they start at?

Hints

Click a Tab to reveal the Hint.

US Version

From the correct cottage, there are several routes that cross each bridge once on the way back to land.

It's OK to visit the same cottage more than once, as long as each bridge is crossed only one time.

UK Version

There are several ways to cross the bridges in order, but there's only one possible island you can start from. It's fine to pass by the same cottage more than once. Look for a route that ends at the mainland after crossing each bridge only once!

US Version

You can try plotting out different routes back to land from each cottage, but there's an easier way to identify the correct one.

Look for something that all but one cottage has in common...

UK Version

You can try drawing lines across all the bridges from each cottage in order, but in fact, there's a way to identify the correct cottage at a glance.

Look for something that the islands have in common. The island that the couple should start from is different from the rest.

US Version

Take a close look at how many bridges are connected to each cottage. There's something odd about the number of bridges connected to one of them...

UK Version

Pay attention to the bridges extending from each island.

Apart from one, all the islands follow the same rule. The island that is the exception is the one that the couple should visit by boat.

US Version

There's only one cottage with an odd number of bridges connected to it.

If you figure out which one that is, you'll have the correct answer!

UK Version

There's only one cottage with an odd number of bridges connected to it.

Work out which one that is, and you'll have the correct answer!

Solution

Incorrect

US Version

Take another look at it.

UK Version

Looks like the boat ride's not over yet.

Correct

US Version

Correct!

The couple should paddle out to cottage D to begin their jaunt back to land.

By starting at a cottage with an odd number of bridges, you can cross them all on the way back in.

UK Version

That's right!

The holidaymakers should take the boat to cottage D.

By starting at a cottage with an odd number of bridges, you can cross them all just once on the way back in.

A big thanks to http://professorlayton4walkthrough.blogspot.com

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