Neil Sloane of ATT Labs shares some his favorite integer sequences from his online encyclopedia!
Recaman’s Sequence is especially perplexing! Sloane asks: does every number eventually appear?
(No one yet knows the answer!)
In which we conclude our conversation and thwart the wicked King.
In which we discuss mattress preservation, group theory, and the problem of the Wicked King.
We also asked, on this week’s segment how to label the faces of some ordinary dice, with twelve different numbers (we did say different didn’t we?) so that every roll produces a prime number. This puzzle is from the fascinating site www.primepuzzles.net. Don’t peek!
We’ve never discussed the famous “Monty Hall Problem” here (though we did talk about it on the radio before we started podcasting). We recently got an interesting letter that highlights the difference between a game like “Let’s Make A Deal” and a game like “Deal or No Deal”.
Mark A. recently wrote us:
Read the rest of this entry »
I had a dream last night involving — (?) well I am not really sure, except that it left me wondering if there is a simple proof (if indeed it is true) that there must be a common factor of
m choose i = m!/(i! (m-i)!)
m choose j = m!/(j! (m-j)!)
for all counting numbers i,j,m with 1 < i,j < m
Another way to state this same thing is: any pair of entries, on any row of Pascal’s triangle (except for the 1’s on the edges) will have a common factor.
With facts of this sort, often there is a clever way to cast things in terms of counting something a couple of different ways which makes things clear.
Dennis Shasha, author of Puzzles for Programmers and Pros
joins us once again, posing a cake conundrum!
How does this simple trick work?
Ask a friend to pick, silently, a three-digit number, then “double” it to make a six-digit number. For example, if she picks 412, the new number would be 412412. Then dividing by 7, then by 11, then by 13, presto! The original number!
Interestingly, there is no decent trick for two-digit numbers; and for four-digit numbers the trick is not so great. But for nine and fifteen digits (for the right kind of people only!!) there is a relatively simple variation.
After explaining how the Princess escaped, we pose a simple puzzle from Dennis Shasha’s new book Puzzles for Programmers and Pros.
(In the next post we’ll say a little more about the princess.)
As B Boom wrote, the first pirate can make a proposal that gives him all but 49 (about, depending on the rules) pieces of
the gold. Read the rest of this entry »
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