Professor Layton and the Last Specter/Puzzles 026-050

Caution! This page contains all the hints and solutions for every puzzle from 1 to 25. Scroll carefully or you might spoil the answer of a puzzle for yourself. The solutions are hidden behind spoiler tags, so only take a peek if you're desperate.

Puzzle 026

 * Name: UFO SOS
 * Trigger: Talk to Clarence
 * Location: North Ely Park
 * Chapter: 4
 * Picarats: 65

Description: "One day, I saw a spacecraft hanging motionless in the sky right above me. 'Must be engine trouble,' I thought. The solution was simple. All I had to do was move the spacecraft's energy ball from the left side to the right, and it was as good as new! Think you can do the same?"


 * Hint 1: The flying saucer can be fixed with a minimum of 31 moves. First, move down the two [[File:PLLS_Puzzle_26_Symbol1.png]] on the right. Then line up the two [[File:PLLS_Puzzle_26_Symbol2.png]] shapes in the top-right corner of the ship.
 * Hint 2: Continuing from Hint 1: Collect all four [[File:PLLS_Puzzle_26_Symbol1.png]] in the middle row, moving the two [[File:PLLS_Puzzle_26_Symbol2.png]] shapes to the left and the right as needed.
 * Hint 3: Once all four of the [[File:PLLS_Puzzle_26_Symbol1.png]] are in a row in the middle, return both [[File:PLLS_Puzzle_26_Symbol2.png]] shapes to the top-right corner. After that, try to maneuver the red [[File:PLLS_Puzzle_26_Symbol1.png]] into the bottom-right space and move all of the other [[File:PLLS_Puzzle_26_Symbol1.png]] to the far right. This will give you the room you need to move the energy ball into the top-left corner.
 * Super Hint: Slide the light-blue [[File:PLLS_Puzzle_26_Symbol1.png]] into the bottom-left section. Then, slide the dark-blue [[File:PLLS_Puzzle_26_Symbol1.png]] into the indentation on the left-hand side. Gather the two [[File:PLLS_Puzzle_26_Symbol2.png]] shapes in the middle row, and move the energy ball to the top-right corner. Slide the two [[File:PLLS_Puzzle_26_Symbol2.png]] shapes to the top left, and move the red and yellow [[File:PLLS_Puzzle_26_Symbol1.png]] to the left-hand side. Almost there!

Puzzle 027

 * Name: Floating Cottages
 * Trigger: Talk to Jasmine
 * Location: Murray Street
 * Chapter: 4
 * Picarats: 35

Description: The 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?


 * Hint 1: 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.
 * Hint 2: 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...
 * Hint 3: 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...
 * Super Hint: 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!

Puzzle 028

 * Name: Black and White Cats
 * Trigger: Talk to Hugo
 * Location: Apartment Row
 * Chapter: 4
 * Picarats: 30

Description: You want to display your impressive collection of black and white cat paperweights on this 4x4 grid. You must fill every space, and no row or column can have more than two same-colored cats next to each other. The six cats currently on the grid must remain where they are. How can you fill in the rest of the grid? Touch a space on the grid to place a cat, change its color, or remove it.


 * Hint 1: Any time you spot two adjacent cats of the same color in a row or column, any space next to them in that row or column will need to be filled with a cat of the opposite color.
 * Hint 2: First, concentrate on the placement of the white cats. You can only place a total of four cat paperweights in any single row or column. Once you figure out where the white cats go, you can pretty much fill the remaining spaces with black cats.
 * Hint 3: A white cat must belong in the empty space between the two black cats in the column farthest to the right. Remember, when you have two cats of the same color next to each other in the middle of a row or column, you must place cats of the opposite color on either side of them. Continue placing paperweights according to these rules until the grid is filled in!
 * Super Hint: Put a white cat between the two black cats in the column farthest to the right. Put white cats in the top and bottom spaces of the second column from the left. Put a white cat between the two black cats in the second row from the bottom. Think you can figure out the rest?

Puzzle 029

 * Name: How Old?
 * Trigger: Talk to Finch
 * Location: Crossroads
 * Chapter: 4
 * Picarats: 35

Description: A friend wrote you the following letter: "Our baby girl Nat was born last year in March. If you multiply her age by those of her older sister Kat and brother Pat, the product is 36. If you add all of their ages together, you'll get a sum of 13. Everyone is healthy and happy. Write back soon!" The letter was written on April 25th. What are the ages of Nat, Kat, and Pat?


 * Hint 1: You should be able to work out Nat's age easily. You know the month in which she was born last year, but when was the letter written?
 * Hint 2: Nat is one year old. When you multiply that by the ages of Kat and Pat, you need to get 36. Hear are the possible combinations: 1x36, 2x18, 3x12, 4x9, and 6x6.
 * Hint 3: The sum of all three children's ages is 13. The youngest child is 1, so the sum of the two older children's ages must equal 12.
 * Super Hint: Kat and Pat are the same age. You need to find a number that when multiplied by itself equals 36 and when added to itself equals 12.

Puzzle 030

 * Name: Book Stacks
 * Trigger: Talk to Olga
 * Location: Library
 * Chapter: 4
 * Picarats: 35

Description: Someone left a ton of books on the table, and now these two librarians have the unpleasant task of shelving them all again. The librarians are trying to count all the books, but they're stacked so high that neither one can see them all. Using each librarian's point of view, work out how many books are on the table.


 * Hint 1: Make a note of all the books you see using the Memo function. For example, take a look at how many books each librarian can see from her viewpoint. That can help you determine how many books are in the center pile.
 * Hint 2: Next, let's figure out how many books are in the lower-left corner of the table. Can you see which stack that is from the other librarian's perspective?
 * Hint 3: You can also work out the number of books stacked in the top-right corner from the viewpoint of the librarian at the bottom of the screen. That leaves only two piles of books to figure out!
 * Super Hint: The books in the top-left corner can be counted using the top librarian's viewpoint. Don't forget that from her point of view, the stack is on the right. You already know that the bottom-left corner contains only two books, so the three books that she sees must be in the top-left corner.

Puzzle 031

 * Name: Light Height
 * Trigger: Talk to Sebastian
 * Location: Closed Factory
 * Chapter: 4
 * Picarats: 50

Description: A single light hangs from a beam above the floor of this dilapidated warehouse. There are two posts, both of which are a foot tall, separated by a distance of 15 feet. The light casts a 3 foot long shadow from the left post and a 2 foot long shadow from the right post. Figure out how high the light is hanging above the floor.


 * Hint 1: Choose one of the posts, and visualize a large triangle formed between the light, the spot on the floor directly under the light, and the farthest point of the post's shadow. Then imagine a smaller triangle formed between the top of the post, the bottom of the post, and the tip of the shadow. These two triangles are mathematically similar. In other words, the larger one is proportional to the smaller one.
 * Hint 2: Let's say the height of the light equals X, and the distance on the floor between the light and the post on the left equals Y. The shadow cast by the post on the left extends 3 feet. X:(Y+3)=1:3, therefore 3X=Y+3.
 * Hint 3: The shadow of the post on the right is 2 feet long. X:(15-Y+2)=1:2, therefore 2X=17-Y.
 * Super Hint: By combining the solutions from the equations of Hint 2 and Hint 3, you get: 5X=20, therefore X=4. The height from the light to the floor equals X.

Puzzle 032

 * Name: Fit for a King
 * Trigger: Talk to Beth
 * Location: Foyer
 * Chapter: 4
 * Picarats: 35

Description: You have the job of cleaning a king's room in his palace. The king is quite meticulous and has declared that his room be cleaned in a very specific way. There are numbers written on the floor tiles that show the order in which the tiles should be cleaned. Starting from tile 1 and proceeding from tile to tile in the correct order, can you find a way to clean all of the tiles without repeating any? To avoid dirtying the newly-cleaned floor, the last tile you clean must be next to the door.


 * Hint 1: There are several possible routes from tile 1 to tile 6. However, you can't pass over the same tile twice, so you should probably follow the edge of the room before you make a turn.
 * Hint 2: The path from tile 6 to tile 12 will look the same as the path from tile 12 to tile 18.
 * Hint 3: The path from tile 18 to tile 24 is a straight line.
 * Super Hint: If you treat the vertical line that runs down the center of the room as a mirror, then you can clean each side using the same zigzag pattern that you already created!

Puzzle 033

 * Name: Fruit Friends
 * Trigger: Talk to Marilyn
 * Location: Market South
 * Chapter: 4
 * Picarats: 25

Description: Four friends met in town, each with a kind of fruit to share. The first friend bought a bunch of bananas; the second bought a cluster of grapes. They set the fruit down at their feet as the third and fourth friends arrived, bringing with them a grapefruit and a melon. They also laid their foot at their feet but then had to run off as fast as possible. Where did the group meet? Circle your answer on the map.


 * Hint 1: What do a grapefruit and a melon have in common?
 * Hint 2: Fruits come in all shapes and sizes. Some fruits may not be very stable when placed in certain locations...
 * Hint 3: The grapefruit and the melon are both round. They started to roll as soon as they were placed on the ground...
 * Super Hint: A round fruit wouldn't roll if it was placed on flat ground. It only makes sense if they were on some sort of hill.

Puzzle 034

 * Name: Apple Picking
 * Trigger: Check the fruit stall
 * Location: Market Center
 * Chapter: 4
 * Picarats: 30

Description: Time to pick some apples! You have three baskets of three varying sizes, and there are five apples on the tree. Pick all of the apples, making sure that the large basket contains more apples than the medium basket, which in turn must contain more apples than the small basket. Each basket must contain at least one apple.


 * Hint 1: Take a look at the requirements for proper apple storage. The number of apples in each basket descends in the following order: large basket, medium basket, small basket.
 * Hint 2: If you're having trouble, try moving everything around and see what's possible. If you just move apples back and forth, though, you probably won't get very far.
 * Hint 3: Once you realize that you can move the baskets as well as the apples, you're close to solving the puzzle. Try out a few different arrangements with the baskets.
 * Super Hint: The small basket can fit quite easily into the large basket. Maybe that will help you count the apples in each basket in such a way that solves the problem.

Puzzle 035

 * Name: Candy Counter
 * Trigger: Talk to Aunt Taffy
 * Location: Market Entrance
 * Chapter: 4
 * Picarats: 35

Description: You ordered candies in the shape of hearts, clubs, diamonds, and spades. But when the candies arrived, you noticed you received the wrong amounts. The seller claims she sent the correct number of each type, and looking again, you realize she's actually right. How many of each candy did you originally order?


 * Hint 1: Take a close look at the shape of each heart, spade, club, and diamond.
 * Hint 2: Have you noticed the top parts of the spades look very similar to the hearts?
 * Hint 3: It looks like something broke during shipping and then got stuck to some of the other candy.
 * Super Hint: The candy that broke was a diamond. The broken pieces of the diamond then got attached to heart candies, which, in turn, made them look like spades.

Puzzle 036

 * Name: How Many Ones?
 * Trigger: Talk to Tweeds
 * Location: Market Center
 * Chapter: 4
 * Picarats: 40

Description: One day, a little boy who was very curious about numbers thought to himself: "If I were to write out all the numbers from 1 to 120, how many times would I write the numeral 1?" Can you work out the answer?


 * Hint 1: Try writing the numbers down and counting the 1s. Be careful with numbers with more than one 1, such as 11.
 * Hint 2: The single digits are easy. There's just one 1.
 * Hint 3: Think about the double digits. There's one 1 in 10 and two 1s in 11. There's also one 1 for every number from 12 to 19, for a total of eight. There are eight more in 21, 31, 41, 51, 61, 71, 81, and 91.
 * Super Hint: What about the triple digits? There's a single one in 100, and two 1s in both 101 and 110. 111 has three 1s, and there are two 1s in every number from 112 to 119. Are there any numbers you haven't considered yet? Don't forget about the 1 in 120, either.

Puzzle 037

 * Name: Seven Coins
 * Trigger: Talk to Badger
 * Location: Market West
 * Chapter: 4
 * Picarats: 20

Description: Seven gold coins make up a circle. Moving only one coin, arrange them so there are an equal number of heads-up coins as there are tails-up coins. Use the stylus to move just one coin. Tap a coin to flip it over. Think you can make heads or tails of the given situation?


 * Hint 1: Go ahead and play with the coins. You can move any coin around as much as you like.
 * Hint 2: You can move and flip a coin over as much as you want. However, since you have a total of seven coins, there will never be an even number of heads or tails. It'll take more than a coin toss to determine the solution to this puzzle!
 * Hint 3: There are more heads-up coins than there are tails-up coins. You can nearly even the field by flipping over one of the heads-up coins. What else could you do with that flipped coin?
 * Super Hint: Even if you flipped a coin over to make four heads and three tails, you still need to make a head disappear. You are only allowed to flip one coin, but there isn't any rule about using that coin to cover up one of the others...

Puzzle 038

 * Name: Flip Maze
 * Trigger: Talk to Louis
 * Location: Market South
 * Chapter: 4
 * Picarats: 40

Description: This clever toy is actually a double-sided maze. Every time the ball drops through a hole, the board will flip over. Do you think you can make it to the goal?


 * Hint 1: This puzzle is harder than it looks! It would be a lot easier if only you could see both sides of the maze at once. Why not use the Memo function to keep track of the ball?
 * Hint 2: Persistence and perseverance are keys to solving this mind-bending puzzle.
 * Hint 3: From the starting point, choose the topmost hole of the two available holes. This fork in the path is one of the most crucial in the maze.
 * Super Hint: Assuming you followed the previous hint, guide the ball through the leftmost hole. Common sense and a little elbow grease will help you reach the goal from there.

Puzzle 039

 * Name: Raven Medals
 * Trigger: Talk to Nabby
 * Location: Market North
 * Chapter: 4
 * Picarats: 35

Description: "If you want to know what's going on in the black market, you need to form these medals into a raven. Using the engravings in the frame as a guide, slide the medals into their correct slots. Oh! That reminds me. Put the stone numbers into their correct spots, too!"


 * Hint 1: Start off with the numbers. Move the 2 and the 3 to the left- and right-side openings in the middle row, respectively.
 * Hint 2: Continuing from Hint 1: Slide the tail medal into the top-right corner, move the heart medal next to it, and move the raven's right wing below that. Keep in mind that the raven is facing you, so don't confuse which wing is on which side.
 * Hint 3: Continuing from Hint 2: Slide the 3 to the bottom-right space, the left wing to the far-right space in the middle row, and the 2 to the space in the bottom-left corner. Next, move the right wing to the far-left space in the middle row, the heart to the bottom row, and the tail to the space above that.
 * Super Hint: Continuing from Hint 3, move the left wing to the top-right space. Replace that vacant space with 1. Then slide the right wing to the top-left space and the tail to the left space in the middle row. Surely you can complete the raven now! Arrange the numbers, and you're done!

Puzzle 040

 * Name: Fill 'er Up
 * Trigger: Talk to Badger
 * Location: Forest Path
 * Chapter: 5
 * Picarats: 40

Description: You are tasked with filling a reservoir by pumping water from a nearby lake using these four pumps. If you filled the reservoir using only one pump at a time, pump A would take three days, pump B would take 6 days, pump C would take 10 days, and pump D would take 15 days. You decide to get one extra pump to make your life easier. Which pump should you buy another of in order to get the job done in exactly one day?


 * Hint 1: How much of the reservoir can each pump fill in one day? Is there any convenient way to add these amounts together?
 * Hint 2: This puzzle can be solved by adding fractions together. If you dislike working with fractions, you can solve the problem by imagining the full reservoir has a certain amount of water in it.
 * Hint 3: Pump A can fill the reservoir in three days. Therefore, it fills a third of the reservoir in one day. Pump B takes six days, so it will fill a sixth in one day. Pumps C and D also follow the same logic. You should be able to work out what the remaining fraction is required by adding them together.
 * Super Hint: Adding a third, a sixth, a tenth and 1/15 gives exactly two thirds. Therefore, the reservoir requires a further third to be full. Which of the pumps is capable of providing that amount of water in one day?