In Professor Layton and the Miracle Mask, are there multiple solutions to the Alchemist's Lair 08 downloadable puzzle?

I find that the four flasks in the bottom right corner should be able to be connected in 3 different ways. But when i tried another one the flasks turned red even though the number of tubes was correct :S

(spoiler) Solution: http://professorlayton5walkthrough.blogspot.se/2012/09/dailypuzzle063.html

Edit: Explanation of the puzzle:

1. Touch a flask and slide to another flask in a direct horizontal or vertical line to connect the two flasks with a glass tube.

2. You can use up to two tubes to connect a pair of flasks. No tubes can cross each other. Touch a tube to remove it.

3. Each flask is numbered to show how many tubes it needs. Once you have enough, the number and flask will turn blue. Too many, and thet will turn red.

4. The alchemy experiment will succeed when all the flasks turn blue and are connected with glass tubes.

In Professor Layton and the Miracle Mask, are there multiple solutions to the Alchemist's Lair 08 downloadable puzzle?

I find that the four flasks in the bottom right corner should be able to be connected in 3 different ways. But when I tried another one, the flasks turned red even though the number of tubes was correct. :S

(spoiler) Solution: http://professorlayton5walkthrough.blogspot.se/2012/09/dailypuzzle063.html

Explanation of the puzzle:

1. Touch a flask and slide to another flask in a direct horizontal or vertical line to connect the two flasks with a glass tube.

2. You can use up to two tubes to connect a pair of flasks. No tubes can cross each other. Touch a tube to remove it.

3. Each flask is numbered to show how many tubes it needs. Once you have enough, the number and flask will turn blue. Too many, and they will turn red.

4. The alchemy experiment will succeed when all the flasks turn blue and are connected with glass tubes.