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A Sweeping Solution is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

This hotel has a suite with many rooms in it. Cleaning such a large suite is quite a task, so the hotel staff likes to take an efficient route that allows them to cover the whole suite without doubling back through any of the rooms.

They take a different route each day, but no matter which order they lean in, there's always one room they pass through at the same point in the route.

Can you work out which one?

Hints




Click a Tab to reveal the Hint.

You want to find a route through the suite without passing through the same room twice.

Why not start off working out some routes and see where they take you?

No matter which route you take through the rooms, there is one room you will always pass through at the same point in the route.

To make it clearer, try starting from the top-left and top-right rooms and count the rooms as you pass through them. Was there a room that was the same number in both routes?

Actually, you don't even need to trace out any routes to work out this puzzle.

Since there are 13 rooms in all, you have to pass through the same room at the seventh room. The twosomes in the middle of the suite are connected by only one door, so one of these rooms must be the central seventh room in any route.

Considering the layout of the suite, we can suppose that one of the two large central rooms in the seventh one that comes up in the middle of any route through the 13 rooms. That room would have to have six rooms on either side of it, wouldn't it?

Which room is that?


Solution

Incorrect

Too bad.

Have you considered all the possible routes?

Correct

Correct!

The large central room on the left hand side is the only room that stays in the same position no matter the route.

Use the wall between the two central halves to divide the suite into two halves. There are several routes, but no matter whether you start on the left or the right, this room will always be the seventh room you pass through.

A big thanks to http://www.youtube.com/user/LaytonKyouju