Puzzle No. 030
Picarats: 30


Have you heard of one-line puzzles? The idea is to place your pen to paper and draw a shape without lifting your pen from the pad or retracting any part of the line. You can, however, cross lines.

Now that you're familiar with the concept, look at the four pictures below. One of them cannot be drawn  with one line.

Which one is it?














Hint One: Each picture should be composed of lines that meet at different points.

With these pictures, if you find a single line that runs out beyond the others, you know you have to start your drawing there.

Try tracing the answer out yourself.

Hint Two: Some points may be the convergence point for several lines. You need to think hard about which line to take in and out of the point in order to make the sketches work.

If your pen is entering a point formed by an even number of lines, you will always be able to leave the point via another line.

Hint Three: One of the familiar objects below can't be drawn as a one-line puzzle.

You'd be surprised by how easily some of the more complicated pictures can be drawn in one stroke.

Solution:













Very nice! There's actually a very east way to tell whether or not a given picture has been drawn in one stroke. This method will be revealed to you after you solve one more of these riddles.

Puzzle No. 029
Picarats: 20


Five suspects are called into police headquarters for questioning. They give the following statements,
A: "One of the five of us is lying."
B: "Two of the five of us are lying."
C: "I know these guys, and three of the five of us are lying."
D: "Don't listen to a word they say. Out of the five of us, four are lying."
E. "All five of us are dirty rotten liars!"

The police only want to release the suspects who are telling the truth. How many people should they let go?













Hint One: This puzzle might look like a big mess at first, but it's fairly simple when all is said and done.

Take E, for example, who says everyone is lying. If she is actually telling the truth, then her statement becomes a lie, and she must be ruled out. Yep, E's a liar for sure.

Hint Two: Let's rule out another couple of suspects. If A's statement is true, then three other people should be saying the same thing as A. This is not the case, so A is a liar.

If B is telling the truth, two other suspects should say the same thing as B. Once again, this is not the case, so B must be lying.

Hint Three: So, to sum things up, so far we've proven that A, B, and E are lying. Let's examine the last two suspects.

If three people are lying, the other two suspects should have the same statement, but everyone is saying something different. On the other hand, if four of the five suspects are lying...

Solution:













That's right! Every suspect accused a different number of people. If anyone was telling the truth, it had to be one suspect, no more no less.

The only suspect whose statement fits that condition is D. It looks like he's a free man now.

Puzzle No. 028
Picarats: 30


You are holding an eight-pointed shape with a red dot on it. If you hold the shape so that the red dot is in the position shown in Diagram A, then flip it over, you'll see a black dot as depicted below.

Now, assume you are holding the shape as shown on the left side of Diagram B. Where will the black dot be when you flip the shape over?

Draw a circle around where you think the black dot should go.













Hint One: If you flip the shape in Diagram A, you get the shape shown in the upper-right part of the screen. Try to visualize where that black dot is when the white side is up.

Diagram B is just a rotated version of Diagram A, so you know that the position of the black dot in Diagram B must also rotate accordingly.

Hint Two: When the shape is positioned as shown in A, the black dot is behind the middle-right prong of the shape. Flip the shape over and you'll see it on the middle-left prong.

See how the dot moves when you flip the shape over? Now think about where that dot should be in the orientation shown in B.

Hint Three: Moving clockwise, when the white side is facing up (as in the left picture of B), the black dot is two spaces ahead of the red dot.

Now you should pretty much know where the black dot it. Just visualize the shape flipping over and you'll have your answer.

Solution:













That's right! Take a look at the diagram for the answer.

Puzzle No. 027
Picarats: 40


Six brothers have gathered around a table to eat dinner. Each of the brothers is prone to fighting with the siblings directly above and below him in age and can't be seated next to either of them. Also, Brothers 3 and 5 got into an argument the other day and refuse to sit next to each other.

The eldest brother (Brother 1) has already sat down at the big table and is waiting on the others to start eating. Can you find a seating arrangement that will keep everyone from fighting with each other?















Hint One: Don't spend too much time trying to think it out. Instead, just move those brothers around and see what develops.

There are only three seats Brother 2 can sit in because he can't sit next to Brother 1. Plop him down in any one of those seats and move on to Brother 3. We know Brother 3 can't sit next to Brother 2....And so on and so forth.

Hint Two: This puzzle would be a breeze if it weren't for the spat between Brother 3 and Brother 5. What a pain they are.

Sit Brother 3 next to Brother 1. That ought to keep the little guy in line.

Hint Three: You already know to sit Brother 3 next to Brother 1.

Next, sit Brother 4 directly across the table from Brother 1.

The rest is up to you.

Solution:













Good job!  Sit the boys as shown and there shouldn't be any trouble. The mirror image of this seating arrangement is also a valid answer. Finally, a meal in peace.

Puzzle No. 026
Picarats: 20


A glass jar holds a single germ. After one minute, the germ splits into two germs. One minute after that, the two germs each split again, forming a total pair of four germs. Continuing at this rate, a single germ can multiply to fill this whole jar in exactly one hour.

Knowing this, how long in minutes would it take to fill the jar if you had started with two germs?















Hint One: If one germ becomes two, and two become four, that means that the number of germs doubles each minute.

Hint Two: If you start with one germ, the germ will multiply and fill the jar in one hour.

Starting with one germ, then, how many will you have in one minute?

Read the problem carefully.

Hint Three: Let's take a step back and think.

Your answer is the amount of time is takes for two germs to fill the jar. If it takes one minute for one germ to turn into two, how much additional time is needed to fill the jar?

Solution:













The answer is 59 minutes.

It takes one minute for a single germ to split into two. Therefore, starting with two germs instead of one only saves you one minute.

Puzzle No. 025
Picarats: 25


In the drawing below, 10 coins are arranged to form an equilateral triangle.

The triangle is pointing up right now, but can you get it to point down by moving three of the coins?














Hint One: If you flipped the position of the base and the top rows of the triangle, the triangle would point the opposite direction. But moving the top rows of the triangle requires you to move six coins.

Why don't you try to move the base row?

Hint Two: You don't really think it's impossible to flip the triangle by moving three coins, do you?! Come on now!

Think about it. You can only move three coins. You're dealing with a three-sided shape. This couldn't be a coincidence, now could it?

Hint Three: There are three corners on a triangle. Since the triangle pictured here is pointing upward, only one corner points upward. The other two corners point downward.

You are trying to reverse the direction of the triangle, so why not focus on rearranging the corners?

Solution:













That's right!

The interesting thing about this puzzle is the way the whole triangle changes shape with the simple shifting of a few coins.

The trick is to think about the corners on the first triangle. Then it's east to see the changes you need to make.

Puzzle No. 024
Picarats: 50


On the counter we have a 10-quart pitcher full of milk, an empty seven-quart pitcher, and an empty three-quart pitcher. The pitchers are unmarked, and your task is to divide the 10 quarts of milk so that both the 10-quart pitcher and the seven-quart pitcher are each holding exactly five quarts.















Hint One: You can use the same strategy you used for the juice puzzle on this puzzle

Simply shifting some milk over to one of the smaller pitchers won't get you the five quarts you need. Pay attention to what remains when you pour some milk into the smallest pitcher.

Hint Two: Pour milk from the 10-quart pitcher into the seven-quart pitcher. Then take the contents of that pitcher and pour what you can into the three-quart pitcher. This leaves you with four quarts in the seven-quart pitcher. After that, return the contents of the three-quart pitcher to the 10-quart pitcher and refill the smallest pitcher using the seven-quart pitcher. This should leave you with one quart in the seven-quart pitcher. Next....

Hint Three: Now you should have one quart left in your seven-quart pitcher. Empty the contents of your smallest pitcher into the 10-quart pitcher, then pour the one quart into the smallest pitcher.
You should now have nine quarts left in your ten quart pitcher, so pour seven of them into the middle pitcher. Next take your newly filled seven-quart pitcher and pour the milk into your three-quart pitcher. You should already have one quart in the small pitcher, so...

Solution:

 

 

 

If you keep at it long enough, you'll eventually come across the solution. The shortest possible solution requires nine moves.

Puzzle No. 023
Picarats: 40


Here we have an eight-quart pitcher filled with juice, an empty five-quart pitcher, and an empty three-quart pitcher.

The pitchers are unmarked, and your task is to divide the eight quarts of juice so that both the five-quart pitcher and the eight-quart pitcher are each holding exactly four quarts.














Hint One: This puzzle can be frustrating because it's easy to end up back where you started.

Pay special attention to difference, particularly the one-quart difference between five quarts and four quarts.

Hint Two: If you pour the contents of the five-quart pitcher into the three-quart pitcher, you are left with two quarts.

If you're aiming to isolate four quarts, you just need to remove one quart from five. To get that one quart, you just need to create a single quart's worth of space in another pitcher.

Hint Three: If you pour the contents of the five-quart pitcher into the three-quart pitcher, you are left with two quarts. Next, empty the three-quart pitcher and pour in the two quarts you had stored in the five-quart pitcher.

Well, look at that! How many quarts worth of space do you have left in that three-quart pitcher now?

Solution:

 

If you keep at it long enough, you're sure to come across the solution. The shortest possible solution requires seven moves. These liquid distribution problems have been around for ages, and have even been spotted in Japanese texts from hundreds of years ago.

 



Puzzle No. 022
Picarats: 30


Seven prizewinning pigs are lazing about in a pen.

To make sure that the pigs don't fight with each other, you've decided to section off the pen with three ropes.

Can you hitch the ropes up to some of the posts shown below and separate each pig from its neighbor? Remember, not even a snout or curly tail can sneak over each partition!














Hint One: Since you have seven pigs to separate and only three ropes, it's pretty much a given that the ropes will have to overlap in places.

Go ahead and hitch the ropes up a couple of times. You might just find the answer.

Hint Two: Look at how the seven pigs are arranged. Do you see the one pig in the middle? In order to separate him from the other pigs, you're going to have to surround him with rope on all sides.

Your three ropes need to be arranged in such a ways that they surround and isolate the middle pig.

Hint Three: Arrange your three ropes so that the little pig in the middle is surrounded completely.

Next, look at how your ropes are laid out. You need to keep the middle pig surrounded, but you also need to separate the other pigs. There aren't many configurations that will satisfy those conditions, so you should have an answer before you know it.

Solution:













Good job! You've made a lot of pigs very happy!

Puzzle No. 021
Picarats: 30


A man has been prescribed 10 pills. Starting today, he must take one pill a day, but because the concentration of the medicine is different in each pill, he must take them in a specific order. Since the pills all look the same, the man has decided to write number on each pill to help him remember the order he needs to take them in.

How many pills does he have to number if he wants to keep track of the order?














Hint One: If the man wants to indicate the order in which he needs to take his pills, he just needs to write a number on each of the 10 pills. While that's true, the bare minimum of numbers he needs to write is fewer than 10. Think about how he can accomplish this.

Hint Two: When you have two visually identical items, you only need to mark one of them. Therefore, you don't need to mark each pill to tell them apart.

Hint Three: Keep in mind that the man must start taking his pills today. In fact, he's going to start by taking the pill right in front of him.

If that's the case, does he really need to mark which pill he's going to take today?

Solution:














Good job!

Since the man has to start taking his medicine today, the first thing he should do is take today's pill. Next, he should label the pills for days two through nine. If he does this, he shouldn't have to label the pill for the last day; it will be the only one withoug a label.

He only needs to label eight pills.

Puzzle No. 20
Picarats: 50



Draw a path between one man's home and his work by connecting matching blocks. The catch is that these met can't stand each other, so you have to make sure that one of the paths touch.

To make a path, all you need to do is tap a block and start drawing.















Hint One: You might think that this puzzle is impossible but rest assured, it's not. The first thing you should try to do is connect any pair of blocks. That will limit where your next path can go. B's route is shortest. Try enough times and you're sure to figure it out.

Hint Two: The path between the b blocks is a straight line D goes around to the north.

Hint Three: As stated earlier, connect the pair of b blocks with a straight line. Then connect the d blocks by drawing a path that arcs up over the b block path. A goes south then east.

Got it now?

Solution:













That's right! Now those guys don't even have to look at each other! Good job!

Puzzle No. 19
Picarats: 30



The Laytonmobile, the professor's pride and joy, is stuck behind several other cars trying to exit a crowded parking lot. Things are so tight, though, that each car can only move forward and backward with respect to the direction it's currently facing.

Use your stylus to direct traffic and guide the professor's red car to the exit.















Hint One: Just trying to clear the cars immediately in front of the professor's vehicle won't get you anywhere. Think about exactly what it is you'll need to do to clear a path to the lot exit.

Hint Two: Don't be afraid to take a step back to move ahead two steps. You may need to move some things into the way to get them out of the way in the end.

When you're moving cars around, be sure to keep in mind each car's directional imitation.

Hint Three: To start, you'll need to move the two cars directly in front of the Laytonmobile. In order to do that, you'll first need to move the horizontally oriented car that sits right above those two vehicles.

Once you've completed that task, move the Laytonmobile forward toward the exit. Then try to rearrange cars at the end of the lot opposite the exit.

Solution:





 Move the horizontal truck above the red car up.












 Move the vertical truck to the right of the red car up.











 Move the vertical truck to the right of the red car up.










 Move the red car right.












 Move the bottom left vertical truck up.











 Move the bottom left horizontal truck left.










 Move the bottom left horizontal truck left.












 Move the topmost vertical truck down.

Move the red car left.



 Move the right vertical truck down.











Move the top horizontal truck left.










 Move the vertical truck to the left of the red car up.










 Move the vertical truck to the left of the red car up.













 Move the red car to the exit.







Good job clearing out the traffic. If you used these steps, you solved the puzzle with the fewest number of steps!