Hey, guys, I just HAD to post these problems.
The first two are my favorites, but they all deserve to be here:
==> same street <==
Sally and Sue have a strong desire to date Sam. They all live on the same street yet neither Sally nor Sue know where Sam lives. The houses on this street are numbered 1 to 99.
Sally asks Sam "Is your house number a perfect square?". He answers. Then Sally asks "Is is greater than 50?". He answers again.
Sally thinks she now knows the address of Sam's house and decides to visit him. When she gets there, she finds out she is wrong. This is not surprising, considering Sam answered only the second question truthfully.
Sue, unaware of Sally's conversation, asks Sam two questions. Sue asks "Is your house number a perfect cube?". He answers. She then asks "Is it greater than 25?". He answers again.
Sue thinks she knows where Sam lives and decides to pay him a visit. She too is mistaken as Sam once again answered only the second question truthfully.
If I tell you that Sam's number is less than Sue's or Sally's, and that the sum of their numbers is a perfect square multiplied by two, you should be able to figure out where all three of them live.
==> Josephine <==
The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first.
THE KINGDOM OF MAMAJORCA, WAS RULED BY QUEEN HENRIETTA I. IN MAMAJORCA WOMEN HAVE TO PASS AN EXTENSIVE LOGIC EXAM BEFORE THEY ARE ALLOWED TO GET MARRIED. QUEENS DO NOT HAVE TO TAKE THIS EXAM. ALL THE WOMEN IN MAMAJORCA ARE LOYAL TO THEIR QUEEN AND DO WHATEVER SHE TELLS THEM TO. THE QUEENS OF MAMAJORCA ARE TRUTHFUL. ALL SHOTS FIRED IN MAMAJORCA CAN BE HEARD IN EVERY HOUSE. ALL ABOVE FACTS ARE KNOWN TO BE COMMON KNOWLEDGE.
HENRIETTA WAS WORRIED ABOUT THE INFIDELITY OF THE MARRIED MEN IN MAMAJORCA. SHE SUMMONED ALL THE WIVES TO THE TOWN SQUARE, AND MADE THE FOLLOWING ANNOUNCEMENT. "THERE IS AT LEAST ONE UNFAITHFUL HUSBAND IN MAMAJORCA. ALL WIVES KNOW WHICH HUSBANDS ARE UNFAITHFUL, BUT HAVE NO KNOWLEDGE ABOUT THE FIDELITY OF THEIR OWN HUSBAND. YOU ARE FORBIDDEN TO DISCUSS YOUR HUSBAND'S FAITHFULNESS WITH ANY OTHER WOMAN. IF YOU DISCOVER THAT YOUR HUSBAND IS UNFAITHFUL, YOU MUST SHOOT HIM AT PRECISELY MIDNIGHT OF THE DAY YOU FIND THAT OUT."
THIRTY-NINE SILENT NIGHTS FOLLOWED THE QUEEN'S ANNOUNCEMENT. ON THE FORTIETH NIGHT, SHOTS WERE HEARD. QUEEN HENRIETTA I IS REVERED IN MAMAJORCAN HISTORY.
As with all philosophers Josephine doesn't provide the question, but leaves it implicit in his document. So figure out the questions - there are two - and answer them.
Here is Josephine's second scroll:
QUEEN HENRIETTA I WAS SUCCEEDED BY DAUGHTER QUEEN HENRIETTA II. AFTER A WHILE HENRIETTA LIKE HER FAMOUS MOTHER BECAME WORRIED ABOUT THE INFIDELITY PROBLEM. SHE DECIDED TO ACT, AND SENT A LETTER TO HER SUBJECTS (WIVES) THAT CONTAINED THE EXACT WORDS OF HENRIETTA I'S FAMOUS SPEECH. SHE ADDED THAT THE LETTERS WERE GUARENTEED TO REACH ALL WIVES EVENTUALLY. QUEEN HENRIETTA II IS REMEMBERED AS A FOOLISH AND UNJUST QUEEN.
What is the question and answer implied by this scroll?
Let's see the others:
==> river crossing <==
Three humans, one big monkey and two small monkeys are to cross a river:
a) Only humans and the big monkey can row the boat.
b) At all times, the number of human on either side of the river must be GREATER OR EQUAL to the number of monkeys on THAT side. ( Or else the humans will be eaten by the monkeys!)
==> centrifuge <==
You are a biochemist, working with a 12-slot centrifuge. This is a gadget that has 12 equally spaced slots around a central axis, in which you can place chemical samples you want centrifuged. When the machine is turned on, the samples whirl around the central axis and do their thing. To ensure that the samples are evenly mixed, they must be distributed in the 12 slots such that the centrifuge is balanced evenly. For example, if you wanted to mix 4 samples, you could place them in slots 12, 3, 6 and 9 (assuming the slots are numbered from 1 to 12 like a clock).
Problem: Can you use the centrifuge to mix 5 samples? Which are the numbers of samples you cannot mix?
==> chain <==
What is the least number of links you can cut in a chain of 21 links to be able to give someone all possible number of links up to 21?
==> children <==
A man walks into a bar, orders a drink, and starts chatting with the bartender. After a while, he learns that the bartender has three children. "How old are your children?" he asks. "Well," replies the bartender, "the product of their ages is 72." The man thinks for a moment and then says, "that's not enough information." "All right," continues the bartender, "if you go outside and look at the building number posted over the door to the bar, you'll see the sum of the ages." The man steps outside, and after a few moments he reenters and declares, "Still not enough!" The bartender smiles and says, "My youngest just loves strawberry ice cream." How old are the children?
A variant of the problem is for the sum of the ages to be 13 and the product of the ages to be the number posted over the door. In this case, it is the oldest that loves ice cream. Then how old are they?
==> number <==
Mr. S. and Mr. P. are both perfect logicians, being able to correctly deduce any truth from any set of axioms. Two integers (not necessarily unique) are somehow chosen such that each is within some specified range. Mr. S. is given the sum of these two integers; Mr. P. is given the product of these two integers. After receiving these numbers, the two logicians do not have any communication at all except the following dialogue:
1. Mr. P. says 'I do not know the two numbers.'
2. Mr. S. says 'I knew that you didn't know the two numbers.'
3. Mr. P. says 'Now I know the two numbers.'
4. Mr. S. says 'Now I know the two numbers.'
Given that the above statements are absolutely truthful, what are the two numbers?
If you have a comment on these, don't post it here: give me a private message on SI instead. And I'll say at the end where did I get these from, so to let everyone know where to get more... :) |
