DA. A Cake Conundrum
Dennis Shasha, author of Puzzles for Programmers and Pros
joins us once again, posing a cake conundrum!
Archive for October, 2007
CZ. A Parlour Trick
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.
CY. Number Sleuths
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.)
Follow Up: Escaping the Beast
We can say a bit more about the Princess’s escape.
Amazingly, an optimal path for the Princess is to swim in a half circle of radius 1/8 that of the lake, then dash out to the edge.
We’ll give an analytic proof, but we could give a totally synthetic (geometric) proof as well.
CX. The Princess and A Beast
How can the princess escape the beast waiting on the shore?
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