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Boris and Natasha
Contributed by Todd
Proebsting and Rustan Leino
Boris and Natasha live in different cities in a country with a
corrupt postal service. Every box sent by mail is opened by the postal
service, the contents stolen, and the box never delivered. Except: if
the box is locked, then the postal service won’t bother trying to open
it (since there are so many other boxes whose contents are so much
easier to steal) and the box is delivered unharmed.
Boris and Natasha each has a large supply of boxes of different
sizes, each capable of being locked by padlocks. Also, Boris and
Natasha each has a large supply of padlocks with matching keys. The
padlocks have unique keys. Finally, Boris has a ring that he would like
to send to Natasha. How can Boris send the ring to Natasha so that she
can wear it (without either of them destroying any locks or boxes)?
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Solution
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The X and Y Dialogue
Contributed by
Josh Benaloh
Two integers x and y are selected such that 1 < x <= y < 100.
Player A is given the product xy and player B is given the sum x+y.
The following dialogue takes place:
A: I don’t know the values x and y.
B: I knew you didn’t know. I don’t know them either.
A: Now I know x and y.
B: Now I know them too.
Can you figure out x and y from this information?
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Solution
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Evening Destinations
Created by
Peter Montgomery
Forty U.S. state names have exactly one word. (See the list below).
Find a non-empty subset of these 40 state names such that every letter
occurs an even number of times in your subset. Upper and lower case are
considered distinct.
Alabama, Alaska, Arizona, Arkansas,
California, Colorado, Connecticut,
Delaware, Florida, Georgia, Hawaii, Idaho, Illinois, Indiana, Iowa,
Kansas, Kentucky, Louisiana,
Maine, Maryland, Massachusetts,
Michigan, Minnesota, Mississippi,
Missouri, Montana, Nebraska, Nevada,
Ohio, Oklahoma, Oregon, Pennsylvania,
Tennessee, Texas, Utah, Vermont,
Virginia, Washington, Wisconsin,
Wyoming
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Solution
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Factor Microsoft’s Zip Code
Created by
Peter Montgomery
Microsoft’s Redmond zip code is 98052-6399. Doing the subtraction gives
91653.
What is the factorization of 91653?
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Solution
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Some Assembly Required
Contributed by
Mike Sinclair
Can you balance seven nails on the upright head of an eighth nail? You
cannot distort the nails or use any other tools or materials. (Except
something to hold the eighth nail upright). All the nails must be the
same size and type.
Know Your Geography
Created by
Peter Montgomery
A woman refuses to travel except through U.S. states whose names begin with
W, O, M, A, or N. Help her get from a Pacific state to an Atlantic
state. When a state name is two words, such as New York, use the first
word.
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Solution
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Which Way Do I Go?
Originated and contributed by
Walter Pullen
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Solution
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A Special Squarish Age
Originated by
Chuck Chan,
contributed by
Rustan Leino
Let’s say that a number is squarish
if it is the product of two consecutive numbers. For example, 6 is squarish, because it is 2*3.
A friend of mine at Microsoft recently had a birthday. He said his age
is now squarish. Moreover, since the previous time his age was a squarish number, a squarish number of years has passed. How many years
would he have to wait until his age would have this property again?
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Solution
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