Starting from Professor Layton and the Unwound Future, throughout the series there are three Puzzle Battles. These are very similar to puzzles as they are brainteasers in which you are trying to find a single correct answer. They are all found in the main story line of the game.
Puzzle Battles are little fights between Professor Layton and couple of other intellectuals Layton comes across. The first Puzzle Battle is against the Future Luke whenever Layton and Luke first meet him at the Gilded 7 Casino. Future Luke proclaims he doesn't believe that Layton is the real one and challenges him to a battle of wits.
Four cards sit in a line.
A heart is next to a diamond.
A club is not next to a spade.
A heart is to the immediate right of a club.
Tap the spade.
Then Future Luke asks Professor Layton to make his own puzzle up. However Professor Layton thinks of an impossible puzzle. Future Luke then catches on to what the professor is doing, and he notices that he is indeed the genuine Professor Layton.
Dimitri Allen vs. Professor Layton
Later on Professor Layton will come across the powerful and menacing Future Professor Layton. Then Future Layton takes off his hat and he turns out to be Dr. Stahngun who is actually Dimitri Allen, a scientist who worked on a time machine 10 years ago. He is the holder of the second Puzzle Battle. During this one, Layton and Dimitri each have five soldiers. Each soldier represented by a flag.
Each troop will engage one troop from the other side in one-on-one combat. Pair each of your red troops against one from the opposing gray forces. Your troops are marked with an icon of Professor Layton. The strength of each troop is represented by the number of stars on its banner.
Arrange your forces so that the red side avoids defeat. When you're ready to submit your answer, tap OK! to proceed.
Professor Layton then finds a way to tie with Dimitri's seemingly unstoppable setup. After they complete their puzzle battle a conversation begins and it is learned that Professor Layton is actually Don Paolo in disguise as he made a deal with the real professor some time beforehand.
Dimitri Allen vs. Professor Layton (2)
The third and final Puzzle Battle is found at the Thames Arms when Professor Layton is about to figure out the answers regarding this so-called Future London. This Puzzle Battle has Professor Layton selecting various spots on a chart given to him by Dimitri. Dimitri plans to escape the Thames Arms by simply walking out of the door. The piece of paper he gave Layton houses the information as to where the bombs that Dimitri has placed are located.
Find all the sensors.
The numbers written above and to the left of the map indicate the number of sensors present in each column and row, respectively.
Derive the location of all sensors using the information provided, and mark them on your map.
However one problem with his plan was that the placement of the bombs spelled out "LIE". So that means that as soon as they got up they would explode and die, unless there were no bombs at all. After Layton had ruined Dimitri's escape play he explains the secrets of Future London and reasons for his plans.
The European version of the game has a different version of the third and final Puzzle Battle. It has the same concept, but has a slightly different design and wording.
Find all the bombs.
The numbers written above and to the left of the map indicate the number of bombs in each column and row. Red dots indicate people and squares indicate tables. There are no bombs in these squares.
Derive the location of all bombs using the information provided, and mark them on your map.
The puzzle is actually solved differently as there is a different design. Instead of LIE, this shows ∞ (the symbol for infinity). Luke mistakes this for the time left before the bombs exploded.
When Hershel and Emmy Altava is on their way to the Triton Estate. They found the bridge tied off with a rope which leads to the part of the town where the estate is.Emmy suggest to hack and slash their way through while Layton suggest a one cut.(which he already figure it out)
The first Puzzle Battle in Miracle Mask begins during Layton and co.'s confrontation with Frankie on the road to the Ledore estate. Connor steps in to settle the dispute peacefully, proposing a simple cup-and-ball puzzle to decide whether the three would continue or not.
Both Luke and Emmy try first, and both lose to Frankie. Layton, working out the trick behind the puzzle, takes his turn and asks to pick his choice before Frankie, and wins. Both Frankie and Connor storm off in a rage.
When Luke and Emmy ask how he did it, Layton explains that the trick behind the puzzle was that Connor would subtly point at the tumbler that the ball was underneath, hence why Frankie kept picking the correct one.
After visiting Alphonse Dalston, the trio head up to the Monte d'Or police station where they attend a meeting. Layton must answer the questions given by each police investigator (Bloom, Grosky and Sheffield in order to find out how the Masked Gentleman's miracles happen. Once solved, they can continue with their investigation