Professor Layton and the Curious Village/Puzzles 51-75

Puzzle 051

 * Name: The Town Barbers
 * Trigger: Talk to Zappone
 * Location: Crumm's Cafe
 * Chapter: 4
 * Picarats: 10

Description: A certain town has only two barbers in it. There aren't any other towns nearby, so everyone who lives there gets their hair cut by one of these two stylists. Looking at these two fine gentlemen, which one should you go to for a haircut?


 * Hint 1: You don't cut your own hair, do you?
 * Hint 2: Everyone in this town has one of these two handsome men cut their hair. The two barbers themselves are no exception to that statement.
 * Hint 3: Since they don't cut their own hair, the miserable haircut Barber A received must have been inflicted upon him by Barber B. Poor guy.

Answer: A

Puzzle 052

 * Name: Find a Star
 * Trigger: Talk to Pauly
 * Location: Northern Hill
 * Chapter: 4
 * Picarats: 30

Description: A star the same shape and size as the one shown on the right is hidden somewhere in this picture. Trace its outline below.


 * Hint 1: There's no way around it! You're just going to have to search this picture long and hard for the answer. Only a star with the exact shape and size as the example star will do! No defective, misshapen, or distorted stars will be accepted!
 * Hint 2: Pay special attention to the left side of the picture.
 * Hint 3: Have you tried searching in the upper-left corner yet?

Answer: The star is in the upper-left side of the picture. The center of the star contains a five-sided black shape and a four sided white shape. When combined, these points form a hexagon. The points of the star radiate outward from each side of this hexagon.

Puzzle 053

 * Name: Fish Thief
 * Trigger: Talk to Agnew
 * Location: Market
 * Chapter: 4
 * Picarats: 35

Description: When you weren't looking, someone came by and gobbled up your fish dinner. The three brothers near the scene of this dastardly crime had this to say: A:"Me? Oh yeah, I ate it. It was good too!" B:"I saw A eat that fish right up!" C:"B and I didn't eat that fish." One of these three brothers is lying to you, but which one is it?


 * Hint 1: Only one person is lying here, so let's take a closer look at their statements. If you assume A is lying, then A didn't eat the fish. If that's true, odes it support the other two brother' statements, or does it make someone else a liar? Try working things out logically like this in order to find your answer.
 * Hint 2: If B is lying, doesn't that also mean that what A said is...less than accurate? Surely by now you've realized that more than one person could have helped eat this fish, right?
 * Hint 3: Here's a big hint for you. Not one, but two uncouth individuals took part in the consumption of your fish. Think about who those two have to be. Now that you know the truth behind what happened, look at the three brother' statements again and see whose testimony doesn't fall in line with what you know to be true. There's your answer.

Answer: C

Puzzle 054

 * Name: Monster!
 * Trigger: Talk to Giuseppe
 * Location: Market
 * Chapter: 4
 * Picarats: 20

Description: On, no! The town is in grave peril! As you read this, a fearsome monster is launching an attack on St. Mystere! Ward off the beast by stabbing it in the eye! And for goodness' sake, HURRY!


 * Hint 1: At a glance, the picture appears to be filled with glowing objects that could well be eyes. But remember, there's only one monster attacking the village.
 * Hint 2: The monster is huge. In fact, it's so big that it could well cover the whole of the town!
 * Hint 3: Have you figured out where the monster is going to strike from? Look to the skies!

Answer: Stab the sword into the crescent moon. The monster is created by the outline of the village against the night sky. The moon is its eye.

Puzzle 055

 * Name: The Odd Sandwich
 * Trigger: Talk to Beatrice
 * Location: Inn
 * Chapter: Between 4 and 5
 * Picarats: 20

Description: Using scraps left over from your breakfast, you've managed to cobble together a rather oddly shaped sandwich. How many times must you cut the sandwich in order to make it fit neatly in the container?


 * Hint 1: Have you thought of turning the sandwich to get a fresh perspective on the puzzle? it may sound slightly ridiculous, but for you do it right, you might be surprised at how everything comes together.
 * Hint 2: You won't have much success solving this puzzle if all you are doing is looking at the image provided. Try rotating the sandwich 90 degrees to the left or right.
 * Hint 3: This solution is startlingly simple. Rotate the sandwich 90 degrees and cut it. The sections fit together perfectly, like puzzle pieces.

Answer: 1

Puzzle 056

 * Name: The Lazy Guard
 * Trigger: Talk to Stachen
 * Location: Entrance
 * Chapter: Between 4 and 5
 * Picarats: 30

Description: The local museum has an exhibit that spans nine rooms, as shown in the diagram below. The entrance to the complex is marked by A, and the exit is marked by B. The security guard on duty is a bit of a loafer and wants to walk each room of the exhibit while turning as few times as possible. What is the fewest number of turns he can make while still visiting every room? As an example, the diagram below shows a course that involves six turns.


 * Hint 1: First off, pay no mind to the sample path shown on the screen. Here's an additional hint for you. Nowhere within the problem does it say the guard can only enter each room once. It's OK for your path to move back through a previously visited room.
 * Hint 2: Has the layout of the rooms and the sample path shown made you feel like all your turns need to be 90 degrees? This puzzle wants you to find the solution with the fewest number of turns. This means that movement will always be in a straight line, but the angle of any given turn is up to you.
 * Hint 3: There's no reason the guard should have to enter the exhibit at an angle parallel to the room. Consider a path that starts with the guard entering from a 45-degree angle. Don't forget, you can move through the same room twice.

Answer: 2. The guard starts off walking diagonally through the rooms from the upper-left corner to the bottom-right corner. He turns left and goes straight up to the upper-right corner, then turns a second time. He now goes diagonally through the remainder of the rooms and out through the exit. Therefore, he only turned twice.

Puzzle 057

 * Name: Cut Which One?
 * Trigger: Talk to Deke
 * Location: Plaza
 * Chapter: Between 4 and 5
 * Picarats: 30

Description: Below are six linked rings. They may look like a tangled mess, but there is one right that, if cut away, would leave the remaining five rights connected end to end in a long chain. Which one must you cut in order to make the chain? Choose one answer from below.


 * Hint 1: It helps to think about how a chain is formed. To make a chain, you have one ring on each end. Each ring between these two end rings will be connected to two rings. If any of the rings are connected to three or more other rings, there's no way a chain can form.
 * Hint 2: Two rings make up the ends of the chain. Which two rings here look like they could be ends. Remember, end rings are each connected to one other ring.
 * Hint 3: Two rings make up the ends of the chains. If you study the picture closely, you can see that the F ring is only connected to one other ring, the E ring. Meanwhile, the other end ring is the A ring. So, which ring should you cut?

Answer: D

Puzzle 058

 * Name: Get the Ball Out! 1
 * Trigger: Tap on the House of Puzzles' Door.
 * Location: Plaza
 * Chapter: 3
 * Picarats: 30

Description: Can you get the red ball out of the maze? Slide obstructing blocks out of the way to clear a path for the ball. This problem can be solved in as few as 12 moves.


 * Hint 1: If all you want to do is get the ball to the goal, just slide things around and see what happens. However, if you're aiming to solve this puzzle in as few moves as possible, you'll have to think ahead. Remember that moving one block immobilizes others.
 * Hint 2: Only blue blocks can move at the beginning. Slide the one on the right up, and then arrange the two purple blocks underneath it in a horizontal line. Next, move the lower yellow block over to the right. This will give you some space to work with on the left.
 * Hint 3: If you've followed the previous hint, you should start to see the answer to the puzzle. In order to move the yellow block that's directly beneath the ball, you're going to have to move that green block on the left. To do that, go ahead and move the bothersome blue block out of the way. Got it now?

Answer: This puzzle can be solved in 12 moves. First, move the blue block on the right up. Move the top purple block up and left in one move, then move the lower purple block up as far as it will go. This allows you to move the lower yellow block to the right. Now move the left blue block left and down as far as it will go in one move. The green block is now free to move down as far as it can. Next, move the upper yellow block left. Move the ball down as far as it will go. The top yellow block needs to slide back to the right. The following move raises the green block up as far as it will go. Move the left blue block all the way to the left and move the ball into the hole!

Puzzle 059

 * Name: The Longest Path
 * Trigger: Talk to Marco
 * Location: Manor Road
 * Chapter: Between 4 and 5
 * Picarats: 50

Description: Two boys are playing a game in which the goal is to take the longest route possible from point A to point B, as shown on the map below. The only rule is that no section of road can be traversed more than once. What course should they take in order to cover the longest distance possible between point A and point B?


 * Hint 1: When solving this puzzle, many people think they have the answer on their first try, only to discover otherwise. Try to walk as much of the road as possible on your way to point B.
 * Hint 2: The area that the boys are walking is a square that's more or less composed of long and short sections of road. After you've charted out your course and think you have the answer, take a quick look to see how much road you left untouched.
 * Hint 3: Starting out from point A, head as far to the left as possible. When you reach the left border, start heading south. The longest path you can draw will form an S-shaped line through the middle of the town.

Answer: Start by drawing the path all the way to the left. At the end of the road, draw the line down past the first intersection. At the second intersection, draw the line to the right past the first intersection again. At the second intersection, go up to the first intersection and turn left. When the line hits the wall, go up again, then turn right at the next intersection. Continue the line all the way to the right, then go down when you hit the wall. Go all the way to the bottom-right corner of the neighborhood, then draw the line left and straight to the exit. If you did it correctly, the path should form an S-shape in the center of the neighborhood.

Puzzle 060

 * Name: Weighing Cats
 * Trigger: Between 4 and 5
 * Location: Reinhold Manor
 * Chapter: Between 4 and 5
 * Picarats: 30

Description: There are three different colors of plush cats before you. The color of a cat denotes its weight. Examples 1 and 2 show their relative weights. You have three red cats and four black cats loaded on one side of the scale. On the other side of the scale, there are four white cats and one black cat. Given this setup, will the scale tip left, tip right, or stay level? Tap your answer on the Touch Screen.


 * Hint 1: Use the results of examples 1 and 2 to simplify the relative weight of the groups of cats being weighed. Look closely to find an accurate equivalent.
 * Hint 2: Example 2 shows that two black cats and a white cat equals three red cats. Swap out the red cats for the black and white ones and see what you can figure out now.
 * Hint 3: Example 1 shows you that five black cats equal the weight of four white cats. If you substitute the four white cats on the right side of the scale for black cats, you end up with six black cats. Put that together with what you learned from Hint Two, and you're very close to the answer.

Answer: Left

Puzzle 061

 * Name: Pin Board Shapes
 * Trigger: Talk to Gordon
 * Location: Manor Parlor
 * Chapter: Between 4 and 5
 * Picarats: 40

Description: The cross shape on the pin board below has nine pins inside it and 16 outside it. Remember that example, because now it's your turn to construct a shape on the board. Can you create a cross that has 17 pins inside it and 16 outside it? Feel free to make your cross and size you like.


 * Hint 1: The original shape in this problem is composed of 24 pins. The board contains a total of 49 pins. Subtract the 16 pins on the outside and the 17 pins on the inside and you get 16, the number or pins that will make up your cross.
 * Hint 2: There are only a few ways you can place a 16-pin cross on the board. When you think you're onto something but don't have quite enough space to draw your cross, you should try something a little bit different. Like maybe changing the orientation of your cross...
 * Hint 3: The cross has to be oriented diagonally on the board. Now you just need to decide how big to make your cross. Make sure you draw it to include the right number of pins!

Answer: The cross will be oriented on a diagonal axis. Start with the third pin from the left in the top row. Connect this pin to the pin one row down and one column to the right. This one connects to the pin one row above and one column to the right. Now connect this pin to the pin in the rightmost column, three rows down. The next pin to connect to is one column to the left and one row down, followed by the pin in the rightmost column and three rows from the bottom. Make another leap to the pin in the very bottom of the third column from the right. Half the cross is now complete!

Continue by connecting the line to the pin one row up and one column to the left. Now connect to the pin one row down and one column to the left. This pin connects to the pin in the left-most column and the third row from the bottom. The next pin is one row up and one column to the right. Now connect to the pin in the left-most column and the third row from the top. Finally, connect this pin with the pin you started with. There should be 16 pins on the outside and 17 pins on the inside.

Puzzle 062

 * Name: The Mysterious Note
 * Trigger: Talk to Inspector Chelmey
 * Location: Manor Parlor
 * Chapter: Between 4 and 5
 * Picarats: 40

Description: A detective who was mere days from cracking an international smuggling ring has suddenly gone missing. While inspecting his last-known location, you find a note. The note appears to be nothing more than a series of numbers, but your gut instinct tells you that this note will reveal the name of the crime kingpin. Currently there are three suspects in the case: Bill, John, and Todd. Can you break the detective's code and find the criminal's name?


 * Hint 1: Here's a little pearl of gumshoe wisdom. Te best way to understand something isn't to study it intently from one perspective. Instead, try to approach the problem from a variety of angles.
 * Hint 2: When you feel like you've see all there is about a case, sometimes upending everything can give you a new view on matters. Have you ever considered upending your DS?
 * Hint 3: Hold your DS upside down and take another look at the note. Do you notice anything about the note now?

Answer: Bill

Puzzle 063

 * Name: How Old is Mom?
 * Trigger: Talk to Lady Dahlia
 * Location: Manor Parlor
 * Chapter: Between 4 and 5
 * Picarats: 20

Description: A father and son are having a conversation. The father turns to the son and says: "You know, Son, there was a time when your old man was twice the age of your mother. Of course, the next year, I was only one and a half times her age, but still, that's pretty amazing, eh? If the father is 44 years old, how old is the mother?


 * Hint 1: You just need to find the difference between the father's age and mother's age. At what ages are the two parents separated by two times the age of the mother? There's only one point where the father's age can change from twice the mother's age to 1.5 times the mother's age after one year.
 * Hint 2: For the father's age to change from twice the mother's age to 1.5 times the mother's age in one year, both parents would have had to be very young at the time. Very, very young.
 * Hint 3: When the mother was one year old...

Answer: 43

Puzzle 064

 * Name: Odd Equations
 * Trigger: Talk to Rodney
 * Location: Town Hall
 * Chapter: 5
 * Picarats: 30

Description: Oh, my! It looks like someone has been writing nonsense on the blackboard again. It turns out, though, that under certain conditions, these strange equations are actually correct. Eight minus six equals two. Eight plus six also equals two. Assuming the above to be true, what does seven plus six equal?


 * Hint 1: At first, it might look like whoever wrote this on the board was just terrible at math, but the truth is that just about everyone does calculations like these. Heck, you probably do it just about every day.
 * Hint 2: Eight minus six does, of course, equal two. But under what conditions does adding six to eight equal two?  Here's a hint:when you do math like this, you probably use a commonplace item that many people have on hand.
 * Hint 3: In this particular type of calculation, no two numbers will ever add up to equal a number higher than 12. This is the most common method, and the one you probably use daily. However, some people use a different method of calculation where two numbers can add up to reach totals as high as 24.

Answer: 1

Puzzle 065

 * Name: What's E?
 * Trigger: Tap on the Cat and Mouse (Luke's Puzzle)
 * Location: Clock Tower
 * Chapter: 5
 * Picarats: 50

Description: According to the diagram shown here, A=2, B=3, C=3, and D=4. So what does E equal?


 * Hint 1: What do you think the numbers assigned to A, B, C, and D represent? Talk another look and see for yourself.
 * Hint 2: A, B, C, D, and E refer to sections of the diagram. What separates one section from another?
 * Hint 3: Focus on the edges between sections and the possibilities that arise from that line of thought.

Answer: 5

Puzzle 066

 * Name: Birthday Girl
 * Trigger: Talk to Lucy
 * Location: Clock Tower
 * Chapter: 5
 * Picarats: 60

Description: When asked about her birthday, a young woman gives the following information: "The day after tomorrow, I turn 22, but I was still 19 on New Year's Day last year." When is her birthday?


 * Hint 1: The first thing you should do is determine what day this exchange is taking place. The woman says she's turning 22 in two days, so right now she must be 21.  Hopefully these two points will give you something to go on.
 * Hint 2: The woman will turn 22 in two days, and her birthday, like all birthday, lasts but one day. She also mentions her age last year.  A year, on the other hand, is a much larger period of time to deal with.  In order for her statement to be true, her birthday needs to fall on a particular day.  Think about how the above two fats help to narrow the possibilities.
 * Hint 3: This conversation took place at the very end of the year. if her birthday is in two days, it will have to be after New Year's Eve.  That's right, it will be a new year by the day after tomorrow.

Answer: 1, 2 (January 2nd)

Puzzle 067

 * Name: The Chocolate Code
 * Trigger: Talk to Lucy
 * Location: Clock Tower
 * Chapter: 5
 * Picarats: 40

Description: On Valentine's Day, your gadget-loving, technophile girlfriend gave you a most unusual slab of chocolate. While the jumble of letters looks like nonsense, if you manage to decode the letters written on the chocolate, a message from your sweetheart will appear. What is she trying to tell you?


 * Hint 1: It's rather surprising that your girlfriend would leave you a message via chocolate. It's usually more her style to contact you via digital means.
 * Hint 2: As a self-professed gadget fiend, on more than one occasion she has suffered from the uniquely modern condition of "texting thumb."
 * Hint 3: If you're still stuck, just look at your closest keyboard for a hint.

Answer: Text Me

Puzzle 068

 * Name: Find the Pentagons
 * Trigger: Talk to Gerard
 * Location: Northern Path
 * Chapter: 5
 * Picarats: 40

Description: A number of five-sided shapes are hidden within the picture below. How many can you find? Answer when you think you've found every hidden shape.


 * Hint 1: There are no equilateral pentagons within the shape, so all the ones you do find will have at least two sides with different lengths. Count each one you spot.
 * Hint 2: Count every five-sided shape you can find! Each pentagon you spot can be reproduced on a different section of the picture by rotating the image 90 degrees. That means that for every type of pentagon you find. You've actually found four more pentagons.
 * Hint 3: Surround the square in the middle of the picture with triangles from within the picture to make different pentagons. Make a special effort to look for pentagons formed by attaching multiple triangles to the square in the picture. These are usually the hardest to spot.

Answer: 12

Puzzle 069

 * Name: Chocolate Puzzle
 * Trigger: Talk to Prosciutto
 * Location: Prosciutto's
 * Chapter: 5
 * Picarats: 30

Description: You have a hankering for chocolate, so you buy a huge sheet of 30 chocolate squares. The sheet is five squares long by six squares wide. You can only break the chocolate at the lines that run between squares, and you aren't allowed to stack multiple segments on top of each other. Keeping those rules in mind, what is the fewest number of times you'll need to break the chocolate in order to separate each of the 30 chocolate squares?


 * Hint 1: It's common for people to start thinking about the way they need to break the chocolate in order to achieve the objective at hand. However, the truth is that no matter how you break the chocolate, the answer you arrive at will be the same.
 * Hint 2: Split a sheet of chocolate and you get two segments where there was only one before. If you then break one of your two segments, you get a total of three segments. Your third break, regardless of what segment you choose, will yield a total of four segments of chocolate. Do you see a pattern here?
 * Hint 3: Since you can't break multiple segments of chocolate at a time, you increase the total number of segments you have by one. If you caught on to that, the rest of the problem should be a breeze.

Answer: 29*


 * Please note: the game requires the number 29 but the answer is incorrect. The 30 pieces can be separated with only 20 breaks. The block can be broken into 5 rows of 6 with 4 breaks. Each row of 6 can be broken into 6 pieces with 5 breaks. 4 x 5 = 20

Puzzle 070

 * Name: The Shattered Vase
 * Trigger: Talk to Giuseppe
 * Location: Market
 * Chapter: 5
 * Picarats: 10

Description: Someone knocked over this fabulous vase and shattered it. Fit the pieces together and restore the vase to its original shape. There's one catch, though. Mixed in with the pieces is a single piece from a different vase.


 * Hint 1: You'll get more out of moving pieces around than reading hints, but you did spend a hard-earned hint coin, so here's a small clue. Start by arranging pieces to form the outer edges of the silhouette.
 * Hint 2: Putting together the outside of the vase should be pretty straightforward. Therefore, the extra piece must look like a piece that goes in the center of the vase.
 * Hint 3: If you've completed the entire outline of the vase, you'll only have two parts left over. Try both of them out and see which one fits.

Answer: The top-right piece does not fit in the puzzle.

Puzzle 071

 * Name: Sausage Thief
 * Trigger: Talk to Giuseppe
 * Location: Market
 * Chapter: 5
 * Picarats: 40

Description: Somebody ate the butcher's sausages! Here's what these four boys have to say: A: "B ate the sausages!" B: "D ate them all up!" C: "I didn't eat them,no way!" D: "B's totally lying!" Only one of these rascals is telling the truth and all the others are, needless to say, lying. Can you figure out who ate the sausage?


 * Hint 1: Remember, you want to find the person who ate the sausages, not the people who are lying. To attack problems like these, go through your list of potential thieves, assume that each one is guilty, and see which statements fit in each case.  That should get you started. Good Luck!
 * Hint 2: If you have chosen the right person, then three of the four boys' statements should be false. If you think you've found the culprit, but only two of the four boys' statements turn out to be lies, you haven't found the thief yet.  Here's another valuable piece of information: only one person ate the sausages.
 * Hint 3: All right,after this hint, you'll probably be able to guess the answer without thinking, but here we go. A and B are lying.  Keep that information in mind and you should have your answer in no time.

Answer: C

Puzzle 072

 * Name: The Sound of Silence
 * Trigger: Talk to Percy
 * Location: Plaza
 * Chapter: 6
 * Picarats: 40

Description: Which of these words doesn't make the sound of silence? Note, Rhythm, Rest, Treble, Chord, Scale


 * Hint 1: When you see a group of words that have a similar theme, it's easy to get hung up on their meaning. Instead,look for other ways to interpret the question asked of you. For example, other than a very literal definition what else could "the sound of silence" be referring to?
 * Hint 2: Read each word out loud and pay attention to how they differ from each other. In particular, think about how each word is pronounced.
 * Hint 3: Still Stuck? Think about what letters aren't pronounced.

Answer: Circle Rest and hit SUBMIT

Puzzle 073

 * Name: How Many Squares?
 * Trigger: Talk to Rodney
 * Location: Town Hall
 * Chapter: 6
 * Picarats: 40

Description: This board has 12 dots on it. Your task is to connect these dots to form as many squares as possible. You can use each dot multiple times, and you can orient the squares however you wish to fit them on the board. However, to be counted as a square, each corner must be on a dot. How many different squares can be drawn on the board?


 * Hint 1: You can use a given dot as many times as you like and can orient the squares however you need to to fit them on the board. In other words, you're going to reuse dots, and you should be on the look out for a few diagonally oriented squares.
 * Hint 2: There are three different sizes of squares that you can make on the board. You shouldn't have much trouble finding the smallest squares.  There are five in total.
 * Hint 3: All four of the medium-sized squares are tilted 45 degrees. Can you see them on the board?  Now that you have the above information, all that's left for you to do is find the biggest type of square.  when you know how many of these are on the board, you'll be done!

Answer: 11

Puzzle 074

 * Name: A Broken Window
 * Trigger: Talk to Agnes
 * Location: Market
 * Chapter: Between 5 and 6
 * Picarats: 30

Description: Four kids were playing, and one of them threw a ball right through your window. Here's what they had to say for themselves. A:"Not me! Id didn't break a thing!" B: "Okay, I'll tell the truth. It was me.  I broke it." C: "Don't be mad at A! He didn't do anything!" D: "B didn't break the glass, I swear." You know for a fact that the scamp who broke your window is lying. However, an unknown number of the other children may be lying as well. Can you figure out which one of these darned kids broke your window?


 * Hint 1: This one's sort of a pain, isn't it? The kid who broke the window is certainly lying, bu you can't forget that a number of the other children might be lying as well.  Keep that in mind as you solve this puzzle.
 * Hint 2: We've already established that the child who actually broke the window lied. Therefore, the child who broke the window must have denied breaking the window when confronted.  In other words, B couldn't have broken the window, and D must be telling the truth about B.  By the way, D didn't do it either.
 * Hint 3: If what A said is true, then C must also be telling the truth. That would mean we had four honest children on our hands, which we know to be false.  Either A or C had to have broken the window.

Answer: A

Puzzle 075

 * Name: The Wire Cube
 * Trigger: Talk to Agnes
 * Location: Market
 * Chapter: Between 5 and 6
 * Picarats: 40

Description: You want to create a cube out of metal wiring using the fewest number of wires possible. You can bend each wire as many times as you like, but no portion of the cube can have more than one length of wire running over the same edge. Don't worry about how one wire will connect to the next, because you'll use a soldering iron later on. What is the fewest number of wires required to complete the task described above?


 * Hint 1: Think about a corner of a cube and how many lines meet at that point.
 * Hint 2: Three lines meet at each corner on a cube. Imagine a corner where a single wire forms two of the three lines. The final line in this corner must come from the end of a different wire.  Therefore, in every corner, at least one of the three lines comes from the end of a wire.
 * Hint 3: There are eight corners to a cube. As discussed earlier, every corner in a cube requires at least one end of a wire.  Each wire has two ends, right?

Answer: 4