Tuesday, May 13, 2014
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Einstein's Puzzle
Let us assume that there are five houses of different colors next to each other on the same road. In each house lives a man of a different nationality. Every man has his favorite drink, his favorite brand of cigarettes, and keeps pets of a particular kind.
- The Englishman lives in the red house.
- The Swede keeps dogs.
- The Dane drinks tea.
- The green house is just to the left of the white one.
- The owner of the green house drinks coffee.
- The Pall Mall smoker keeps birds.
- The owner of the yellow house smokes Dunhills.
- The man in the center house drinks milk.
- The Norwegian lives in the first house.
- The Blend smoker has a neighbor who keeps cats.
- The man who smokes Blue Masters drinks bier.
- The man who keeps horses lives next to the Dunhill smoker.
- The German smokes Prince.
- The Norwegian lives next to the blue house.
- The Blend smoker has a neighbor who drinks water.
This is a simple constraint satisfaction problem. Let us start by defining a regular language that consists of all the possible solutions for the puzzle. We need five basic variables: Color of the house, Nationality of the owner, and his favorite Drink, Cigarette, and Pet. We define each variable as the language of the possible values of the variable.
The next concept to define is that of a House. Let us construe it as a concatenation of the five terms defined above:
define Color [blue | green | red | white | yellow];
define Nationality [Dane | Englishman | German | Swede | Norwegian];
style="font-weight: bold;"> define Drink [bier | coffee | milk |tea | water];
define Cigarette [Blend | BlueMaster | Dunhill | PallMall | Prince];
define Pet [birds | cats | dogs | fish | horses];
With five variables each taking one of five possible values, this gives quite a number of possible households, 5x5x5x5x5 = 3125, to be exact. A road with five houses next to each other, House^5, provides an astronomical number of possible combinations of colors, nationalities, drinks, cigarettes and pets.
define House [Color Nationality Drink Cigarette Pet];
To solve Einstein's puzzle, we represent each of the fifteen constraints as a regular language and intersect these languages with the initial set of all possibilities. If all goes well, at the end we will know who keeps fish. For example, we can interpret The Englishman lives in the red house. as $[red Englishman]. This constraint is trivial to encode because in our representation of a house, the color and the nationality are adjacent. The second costraint, The Swede keeps dogs could be represented as $[Swede Drink Cigarette dogs] but we will choose a less verbose formulation, $[Swede ~$Pet dogs], that does not explicitly list the variables that separate Nationality and Pet. The fifteen constraints are shown below.
All that we need to do to solve the problem is to impose the constraints on the row of five houses by intersection. The solution below is almost correct.
define C1 $[red Englishman];
# The Englishman lives in the red house.define C2 $[Swede ~$Pet dogs];
# The Swede keeps dogs.define C3 $[Dane tea];
# The Dane drinks tea.define C4 $[green ~$Color white];
# The green house is just to the left of the white one.define C5 $[green ~$Drink coffee];
# The owner of the green house drinks coffee.define C6 $[PallMall birds];
# The Pall Mall smoker keeps birds.define C7 $[yellow ~$Cigarette Dunhill];
# The owner of the yellow house smokes Dunhills.define C8 [House^2 ~$Drink milk ~$Drink House^2];
# The man in the center house drinks milk.define C9 [? Norwegian ?*];
# The Norwegian lives in the first house.define C10 $[Blend ? ~$Pet cats | cats ~$Cigarette Blend];
# The Blend smoker has a neighbor who keeps cats.define C11 $[horses ~$Cigarette Dunhill | Dunhill ? ~$Pet horses];
# The man who keeps horses lives next to the Dunhill smoker.define C12 $[bier BlueMaster];
# The man who smokes Blue Masters drinks bier.define C13 $[German ~$Cigarette Prince];
# The German smokes Prince.define C14 $[Norwegian ~$Color blue | blue ? ~$Nationality Norwegian];
# The Norwegian lives next to the blue house.define C15 $[Blend ~$Drink water | water ? ~$Cigarette Blend];
# The Blend smoker has a neighbor who drinks water.
The result is a network with five paths. In four of the solutions nobody keeps fish and the German keeps the same kind of pet as someone else. We need one final constraint, presupposed by the question Who keeps fish?:
define Solution [House^5 & C1 & C2 & C3 &C4 & C5 &
C6 & C7 & C8 & C9 & C10 &
C11 & C12 & C13 & C14 & C15];
With C16 added, only one solution remains. To make it easier to see, we compose the solution with the transducer that adds some prose around the pieces along the one remaining path:
define C16 $fish;
# There is someone who keeps fish.
We can now see the solution.
define Describe [House -> "In the " ... .o.
Color -> ... " house " .o.
Nationality -> "the " ... " " .o.
Drink -> "drinks "... ", " .o.
Cigarette -> "smokes "... "s,\n and " .o.
Pet -> "keeps " ... ".\n"] ;
In short, it's the German who keeps fish.
regex [Solution .o. Describe];
76 states, 75 arcs, 1 path.
xfst[2]: print lower-words
In the yellow house the Norwegian drinks water, smokes Dunhills,
and keeps cats.
In the blue house the Dane drinks tea, smokes Blends,
and keeps horses.
In the red house the Englishman drinks milk, smokes PallMalls,
and keeps birds.
In the green house the German drinks coffee, smokes Princes,
and keeps fish.
In the white house the Swede drinks bier, smokes BlueMasters,
and keeps dogs.
Walgreens Likely To Move Their Headquarters Away From The World's Highest Corporate Tax Rate: The U.S.A.
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| We're #1! |
NEW YORK (TheStreet) - Expect Walgreen's (WAG_) to soon say whether the company will move its headquarters outside the U.S. in an effort cut its corporate tax rate. That expected color comes after a handful of large Walgreen's investors began pressing the company to consider a move to a lower-tax jurisdiction as part of its acquisition of European pharmacy giant Alliance Boots.
Walgreen's purchased 45% of Alliance Boots from private equity firm KKR in 2012 for $4 billion in cash and $2.7 billion in stock. The company also agreed to an option to buy the rest of Alliance Boots, in coming years, for $9.5 billion.
While Walgreen's didn't chose to use the first leg of the transaction to invert its ownership abroad for tax purposes, the second leg of the transaction is nearing and investors as prominent as Jana Partners are now pressing for such a move.
On a fourth quarter earnings call, Walgreen's CEO Gregory D. Wasson said, "[Just] to reiterate, as I said on the last call, we have no plans to do an inversion." In that earnings release, Walgreen's forecast its tax rate to be about 37.5%, while Alliance Boots would be around 20%.
Within weeks, shareholders such as Jana Partners then requested a meeting with management to express their frustration, as the Financial Times first reported.
Jana and other investors at the meeting pitched their views on the merit of an inversion and Walgreen's appears to have taken the message, Crain's Business Chicago noted in a report that speculated Walgreen's management might lose its grip of the company through the Alliance Boots deal.
At a Barclays analyst conference on April 30, Walgreen's management changed its tune on an inversion. Such a tax move is being considered, the company said.
"We're evaluating all of that. We are aware of all of the inversions that are happening and certainly all of that is being investigated in Part II," Walgreen's investor relations head Rick J. Hans said. "We've never been a proponent to pay more taxes than we have to. We try to optimize that. It creates value," he added, while noting that there could be costs and benefits to such a move.
Obvious costs would include increased public scrutiny of a move abroad, possible customer defections and government reaction, especially because the pharmacy benefits operations of Walgreen's are a recipient of Medicare and Medicaid-related drug prescription dollars. Benefits would include a tax rate that could drop as low as 20%, according to tax expert Robert Willens.
A part of Walgreen's changing commentary that hasn't been reported on is how quickly a decision may be made. Hans, the Walgreen's IR executive, said at the Barclays conference investors should expect a decision on the possible inversion by late summer or early fall, when the company files its annual proxy to shareholders.
Morning Links 5-13-2014
Trey Gowdy destroys Xavier Becerra over fund raising hypocrisy off tragedies (Video)
"Shut up is Why” The Liberal Debate Society – IFL 2014 #8
Networks Eagerly Push White House Climate Change Agenda Ahead of Obama Interviews
That's Divergent! Actress Tells Time Magazine She's Not a Feminist 'Because I Love Men'
CHICAGO MAYOR RAHM EMANUEL ANNOUNCES CITY JOBS, INTERNSHIPS WILL GO TO ILLEGAL ALIENS
Monday, May 12, 2014
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