Logic Riddles Case 6-10

So, did you have any trouble in solving our previous Logic Riddles? If not, then now we're back with harder puzzles for you to solve. If yes, it's okay, you should still try these riddles anyway, as they're very brain challenging.


Logic Riddle Case 006

So, you've angered the spirit of Halloween by failing to revere the Great Pumpkin, and now a curse has befallen you. On the walkway home, you find a Ward of Seven Jack O' Lanterns arranged in a circle. If midnight comes and any of the seven are still lit, a dark reaper and seven dark horses with seven dark riders shall visit thy abode. They shall surround thy domicile and, while circling it, they will proceed to pelt thy dwelling with eggs and cream of shaving. And come morn there will be a great mess to be reckoned with. So you better get those lanterns out.


Unfortunately, you quickly discover something odd about these lanterns. When you blow out the first one, the lanterns on either side extinguish as well! But there is more. If you blow out a lantern adjacent to one that is extinguished, the extinguished one(s) will relight. It seems that blowing on any lantern will change the state of three - the one you blew on and its two neighbors. Finally, you can blow on an extinguished lantern and it will relight, and its neighbors will light/extinguish as applicable. Frightened by the sound of many hooves, you try to clear your mind and solve this puzzle....

Answer:

The fastest way of turning all the lantern off are by 7 blows. How to do it is by blowing each lantern in order, like this:
You blow lantern 1: 7 (off) - 1 (off) - 2 (off) - 3 (lit) - 4 (lit) - 5 (lit) - 6 (lit)
You blow lantern 2: 7 (off) - 1 (lit) - 2 (lit) - 3 (off) - 4 (lit) - 5 (lit) - 6 (lit)
You blow lantern 3: 7 (off) - 1 (lit) - 2 (off) - 3 (lit) - 4 (off) - 5 (lit) - 6 (lit)
You blow lantern 4: 7 (off) - 1 (lit) - 2 (off) - 3 (off) - 4 (lit) - 5 (off) - 6 (lit)
You blow lantern 5: 7 (off) - 1 (lit) - 2 (off) - 3 (off) - 4 (off) - 5 (lit) - 6 (off)
You blow lantern 6: 7 (lit) - 1 (lit) - 2 (off) - 3 (off) - 4 (off) - 5 (off) - 6 (lit)
You blow lantern 6: 7 (off) - 1 (off) - 2 (off) - 3 (off) - 4 (off) - 5 (off) - 6 (off)
Congratulations! The Great Pumpkin decides to save your soul, just this time though...

Logic Riddle Case 007
Pretend that the above is drawn on a piece of paper, draw 4 lines with an imaginary pen w/o lifting up the pen so that the lines go through all the dots using only 4 lines. How is it done?

Answer:

This is what I called as literally "out-of-the-box" thinking. Nobody told you that you can't draw the line outside your imaginary box of nine dots, right?

Logic Riddle Case 008

A poor but smart farmer is convicted for fraud against rich governor. He gets the death penalty for his crime. The judge allows him to say a last sentence in order to determine the way the penalty will be carried out. If the farmer lies, he will be hanged, if he speaks the truth he will be beheaded. The farmer speaks a last sentence and to everybody surprise some minutes later he is set free because the judge cannot determine his penalty.

What did the farmer say?

Answer:

The farmer said: "I shall be hanged!"

If the farmer was lying, he would be hanged. But that's what the farmer was saying. So he speaks the truth. But if he speaks the truth, he would be beheaded, so then he was not speaking the truth. So it is impossible for the judge to determine wether the farmer speaks the truth or not. So therefore the judge cannot determine the penalty and sets the farmer free.

Logic Riddle Case 009

You manufacture brain wave entrainment CDs for companies that sell self-improvement products. You are at the post office, with ten boxes of them ready to close up and ship out, but you have a problem. Nine of the boxes contain CDs that are designed to put the listener into an "alpha" or relaxing state, and one is full of CDs that are designed to put the user into a deeper "delta" state, for deep sleep. They look identical, and you forgot to label them.

There is one difference, however. You remember that the "alpha" CDs weigh 13 grams, and because different CD blanks were used, the "delta" CDs weigh 15 grams. Unfortunately, you can't feel the difference in weight by lifting them.

The post office does have a scale. It costs one dollar each time you weigh something though, and you want to keep your costs down. How do you use the scale only ONCE to determine which are the "delta" CDs?

Answer:

Label the boxes 1 through 10. Put one brainwave entrainment CD from box number one on the scale. Then, on top of that, put two CDs from box number two. Then put three from box number three on those, four from box four, and so on.

There are now 55 brainwave entrainment CDs on the scale. Pay the dollar and see what the total weight is. If they were all 13 grams, the total weight would be 715 grams (55 x 13). However, you know that one or more of the CDs weighs 15 grams.

Subtract 715 grams from the total weight, and this gives you the "extra weight" for the heavier CDs. Since you know that they are each two grams heavier than the others, you can divide this excess weight by two, and the result tells you how many of the heavier Cd's are on the scale, and this number tells you which box contains the "delta" CDs.

Example:

If the weight is 727 grams, you would subtract 715 from this, leaving you with 12 grams of "excess weight." Divide this by 2, and you know that there are 6 of the heavier CDs on the scale. Since the number of CDs from each box coincides with the number assigned to that box, you now know that box number six has the "delta" brainwave CDs.

Logic Riddle Case 010

It is your task to determine how high you can drop a billiard ball without it breaking. There is a 100 story building and you must determine which is the highest floor you can drop a ball from without it breaking. You have only two billiard balls to use as test objects. If both of them break before you determine the answer then you have failed at your task. What is the order of floors that you should drop the balls from to minimize the number of droppings that you will have to make to determine the answer?

Assume that if a ball doesn't break you can reuse it without worrying about it being weakened.

Answer:
If the proper order is chosen, you can determine the breaking point with a maximum of 14 drops. Here's how to do it:

First drop the first ball from the 14th floor. If it breaks you can determine the exact breaking point with the other ball in at most 13 more droppings, starting at the bottom and going up one floor at a time.

If the first ball survives the 14 floor drop then drop it again from the 27th (14+13) floor. If it breaks you can determine the exact breaking point with at most 12 more droppings.
If the first ball survives the 27 floor drop then drop it again from the 39th (14+13+12) floor. If it breaks you can determine the exact breaking point with at most 11 more droppings.
Keep repeating this process always going up one less floor than the last dropping until the first ball breaks. If it breaks on the x-th dropping you will only need at most 14-x more droppings with the second ball to find the breaking point. By the 11th dropping of the first ball, if you get that far, you will have reached the 99th floor.

That's all about September 2011 hard riddles. We will back in near future with more difficult puzzles.

Difficulty:

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Logic Riddles

• Logic Riddles Case 11-15
• Logic Riddles Case 1-5