Thursday, January 31, 2008

Inspector Beethoven III Riddle

Inspector Beethoven III Puzzle
Handel has been killed and Beethoven is on the case. He has interviewed the four suspects and their statements are shown below. Each suspect has said two sentences. One sentence of each suspect is a lie and one sentence is the truth. Help Beethoven figure out who the killer is.

Joplin: I did not kill Handel. Either Grieg is the killer or none of us is.
Grieg: I did not kill Handel. Gershwin is the killer.
Strauss: I did not kill Handel. Grieg is lying when he says Gershwin is the killer.
Gershwin: I did not kill Handel. If Joplin did not kill him, then Grieg did.

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Sunday, January 27, 2008

How to reject a rejection letter ?

I just happened to stumble upon a beautiful letter basically rejecting the rejection of his application to a post of a professor. The person , for sure had a lot of dejection and a lot of courage and wit to reply back the authorities with an awesome reply. Lets look over it:
Herbert A. Millington
Chair - Search Committee
412A Clarkson Hall, Whitson University
College Hill, MA 34109

Dear Professor Millington,

Thank you for your letter of March 16. After careful consideration, I
regret to inform you that I am unable to accept your refusal to offer me
an assistant professor position in your department.

This year I have been particularly fortunate in receiving an unusually
large number of rejection letters. With such a varied and promising field
of candidates, it is impossible for me to accept all refusals.

Despite Whitson's outstanding qualifications and previous experience in
rejecting applicants, I find that your rejection does not meet my needs at
this time. Therefore, I will assume the position of assistant professor
in your department this August. I look forward to seeing you then.

Best of luck in rejecting future applicants.

Sincerely,
Chris L. Jensen
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Thursday, January 24, 2008

Birbal the Wise Puzzle

Birbal the Wise Puzzle
Emperor Akbar once ruled over India. He was a wise and intelligent ruler, and he had in his court the Nine Gems, his nine advisors, who were each known for a particular skill. One of these Gems was Birbal, known for his wit and wisdom. The story below is one of the examples of his wit. Do you have it in you to find out the answer?

Emperor Akbar was very fond of Birbal as were many of the village people.
However, this made quite a few of Akbar's other ministers jealous.

One day, they decided to come up with a plan to rid them of the "great" Birbal. To avoid suspicion from falling on them, they took the help of the emperor's barber in this plan.

A week later, while Akbar was receiving a haircut, the barber lightly mentioned that he knew of someone who could allow Akbar to reach and even converse with his ancestors who had passed away, but he also stated the man who would go to the heavens would have to be witty, intelligent and wise.
Akbar instantly recommended Birbal for the task.

Birbal was told that a fire would be lit around him and the smoke would carry him to heaven; however, chanting would protect him from burning to his death. Birbal instantly knew that this was a plan to get rid of him, but not wishing to anger the emperor, he agreed to perform this task in a month. During this period of time, he asked some laborers to build a tunnel connecting his house to the cemetery, where the "rites" would be held.

When the day came, Birbal escaped his death by going to his house where he stayed for a month growing out his beard. A month later, he went back to Akbar's palace. When asked about the health of Akbar's ancestors, Birbal replied that they were doing very well but were missing just one thing.

What did Birbal say they were missing in heaven?
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Wednesday, January 23, 2008

Solution to The Exile of Sir Floyd Puzzle

This is the Solution/answer to the The Exile of Sir Floyd Riddle posted on 7th January 2008. If you havent tried it as yet, go for it at The Exile of Sir Floyd Puzzle .

It is not hard to see that if the number of towns is infinite, then Sir Floyd can wander away forever and never return. If you don't believe this, look at the hexagonal tiles on a bathroom floor, and consider the cracks between them to the be roads. Going left, then right, takes you steadily away from your starting point.

So let us rule out the "outlandish" possibility that there are an infinite number of towns. Then it should be clear that Sir Floyd will eventually run out of unvisited towns, and so must reach a town he has already visited.

Now it's possible that he enters this town from a different road than he did the first time he visited it. So let's assume that, in that case, we watch him continue in his exile. Eventually, he must re-enter a town and do so from the same road by which he entered it the first time. From that point on, every step he takes must be a repetition of his initial steps. Where he went right the first time, he must go right the second time, and so on.

Our next question is, is the capital city on this loop? And the answer is, it must be! Because it turns out that if we know which city Sir Floyd is in, and what road he left it by, we can determine which road he entered the city by, and hence what neighboring town he came from. So if we reverse Sir Floyd's steps, we must return to the capital. But the loop has the property that it is a loop both forwards and backwards. There is no way that Sir Floyd could have gone through a few towns that were not on the loop, and then suddenly joined it, because that means that a given town has two roads that Sir Floyd used to enter it, but for which in both cases he left by the same third road, a possibility ruled out by his method of choosing the exit road.

Finally, the same reasoning should convince you that the first time Sir Floyd re-enters a town by the same road, he has just left the capital city (though not necessarily the first time he returned to it!).
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Monday, January 14, 2008

Solution / Answer to The King and the Poison Puzzle

Here is the solution/answer to The King and the Poison Riddle posted on 30th December 2007. For those who haven't yet tried.. have a look at The King and the Poison Puzzle
The treasurer's plan was to drink a weak poison prior to the meeting with the king, and then he would drink the pharmacist's strong poison, which would neutralize the weak poison. As his own poison he would bring water, which will have no effect on him, but the pharmacist who would drink the water, and then his poison would surely die. When the pharmacist figured out this plan, he decided to bring water as well. So the treasurer who drank poison earlier, drank the pharmacist's water, then his own water, and died of the poison he drank before. The pharmacist would drink only water, so nothing will happen to him. And because both of them brought the king water, he didn't get a strong poison like he wanted.

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Saturday, January 12, 2008

The Dither Puzzle

The Dither Riddle
In the country of Oopsylvania, the unit of currency is the dither. Originally, there were three denominations of coinage, worth 1 dither, 5 dithers, and 7 dithers. However, it was discovered that the 1 dither coins included a dangerous amount of arsenic, and so one day, an emergency decree was issued and all the 1 dither coins were suddenly withdrawn.

The gum man, whose packages of gum sold for 1 dither, called an emergency meeting that night with other vendors whose business was also affected by the change. "What are we going to do?", one person cried. "There is no way for me to sell my necklaces, which cost 2 dithers. I will have to try to bundle them together."

"My brooms cost 3 dithers, and the dust pans are 4 dithers. No one can pay this price now, since the 1 dither coins are gone. What are we to do?"

"I'm not worried," said the pie man. "All my pies cost 5 dithers, so everyone who wants one can buy. And I may even sell more pies, since some of your goods have prices that are impossible to pay now!"

"Oh what am I to do?" said the onion seller. "My goods cost 6 dithers, but can't be paid for."

"At least you would only lose 1 dither if someone gave you a 5. But each of my chairs costs 9 dithers, and there's no way I can afford to accept a 5 dither coin, or even a 7 dither coin, for them," cried the caner.

"People, please calm down! Let us try to get a handle on this!" shouted the gum seller. "Until a replacement for the old 1 dither coins is available, we must adjust. But still, some prices can be paid. After all, just using the 5 dither coin, we can pay 5, 10, 15, 20 dithers or any multiple. Similarly, using the 7 dither coin gives us many more prices, 14, 21, 28 and so on. In fact, I see now that there are infinitely many prices that are still manageable."

A young cross-eyed fellow with unruly hair stood up, and cleared his throat before speaking. "May I have your attention? I think things are really not that bad at all. In fact, not only are there infinitely many prices we can charge, but there are not very many prices we can't charge. I've just worked out a way to make every price from 100 dithers up to 200 dithers." And with that he began reading a table as follows:

100 = 20 * 5
101 = 16 * 5 + 3 * 7
102 = 19 * 5 + 1 * 7
103 = 15 * 5 + 4 * 7
104 = 18 * 5 + 2 * 7
105 = ...


"Stop!" yelled an old woman. There is no need to continue. What you have just told us is enough to show that every price from 100 dithers upward can be formed. Now all we need to do is work downwards and see what prices below 100 dithers are missing."

1. Are there really only finitely many "missing" prices?
2. If so, what is the highest missing price?
3. Why did the old woman believe that the partial list, from 100 to 104, was enough information?
4. What prices are missing?
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Monday, January 7, 2008

The Exile of Sir Floyd Puzzle

The Exile of Sir Floyd Puzzle
Sir Floyd was an amorous knight, it was little surprise when he was caught wooing the king's daughter Mitzi. The king was quite angry, but being a merciful monarch, he decided merely to exile Sir Floyd.

He put it to him this way:

"It is my wish that you leave this town by any road you choose, and move to a neighboring town. You may stay there a single night. The next day you must set out to a neighbor of that town, where again you may stay a single day, and so on for eternity."

Princess Mitzi silently handed him a map of the kingdom. Sir Floyd opened it up, and saw that every town in the kingdom sat at the junction of three roads, each of which led to another town in the kingdom. None of the roads crossed on their way from one town to another.

"A man could truly get lost forever in such a rat's maze!" said Sir Floyd.

"I have a suggestion," whispered Princess Mitzi. "Tonight, choose any of the three neighboring towns as your goal. Tomorrow, choose your next town by taking the leftmost of the two roads you have not traveled. From the following town, leave by the rightmost of the two roads, and alternate in this manner."

"Now go", thundered the king, "and I hope never to see you again!"

"Now go," whispered Princess Mitzi, "and I pray that you will return!"

What are the chances that Sir Floyd will return? What (outlandish) loophole must you rule out to make your calculation?
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Saturday, January 5, 2008

Solution to the Urn Puzzle

This is the solution / answer to the Urn Puzzle posted on 4th November 2007. Those who haven't yet tried , first give it a try at Urn Puzzle
The last ball is white.

The number of white balls in the urn is an odd number at the beginning of the process. On each step, two balls are tentatively removed from the urn. But it is never the case that this results in exactly one white ball being permanently removed; if a black and white are removed, the white is returned. If two whites are removed, both are taken.

In other words, if the number of white balls was odd before a move, it is still odd after the move. Hence, since we started with an odd number of white balls, we must end with an odd number of white balls. Since we only have one ball left, that must be white.
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