On Thursday I'll be heading up to Baltimore to give a talk at Johns Hopkins University. I'll be discussing an old favorite: The Monty Hall Problem! Actually, it's been about two years since I've given a talk on that particular subject, so it will be nice to have an excuse to revisit it.
From there it will be a quick shot up 95 and the NJ Turnpike to spend some time working out of my New Jersey office. Which is to say I'll be spending Thanksgiving with my parents and brother. Should be fun! I don't anticipate blogging from the road, however, so things will be even sleepier here than usual, for a while.
The final POTW has been posted. A bit of a joke problem to wrap up the term, but one that can be fun to mull over at odd moments. Thanks to everyone who has been contributing to the comments on those posts. I'm open to suggestions for good themes for future terms. Keep in mind that I try to keep the problems at a level where it is not just math majors who can participate. So, “abstract algebra” or “point-set topology” would not be good themes.
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I can think of three answers to the POTW, but I'm pretty sure two of them are not what you had in mind...
Another Matt,
I have come up with at least 5 potentially valid "solutions". Of course, only one of those is what Jason had in mind. The problem called for a number, not an integer (or even a real number!), and it said alphabetical order. Technically zyxw is in alphabetical order, just the reverse of the normal alphabetical order. Those should be enough hints to get the other four solutions.
Oh, right, reverse alphabetical. However, Jason calls out one (1) of them as not counting, so it looks like we can't have our pie and eat it too.
Well, that shoots down two of my "solutions". It's a shame, because all four of them (along with a - sign) appear in a fairly famous (to those with some mathematical background, anyway) formula. "One" was actually one of the "solutions" I was considering.
A well-euled formula, no doubt.
Indeed it is! We are past the due date, so I'll share my "solutions", which of course are e and i (obviously in alphabetical order, since they are only a single letter), pi and one (which are only "solutions" if backwards alphabetical order is permitted).
Arriving at the real solution was also pretty simple once you give it some thought. It cannot be a number with more than two digits since the words "hundred" and "thousand" don't meet the criteria, and any words containing "-illion" don't as well. (That excludes million, billion, etc.). Focusing on one or two digit numbers then, all single digit numbers fail to meet the criterion. All two digit numbers greater than 19 not ending in zero, therefore are also excluded (all contain one of the single digit numbers in their name). The "teens" are all excluded. That leaves 11, 12 and the two digit numbers ending in 0. Eleven and twelve obviously don't fit, so it must be a two digit number ending in 0. 60, 70, 80 and 90 are immediately eliminated (they all have the associated single digit in their names). That leaves only 5 candidates: 10,20,30,40 and 50. By inspection, only "forty" fits the criterion and is thus the correct solution.
As always, thanks for the feedback. You're right that I should have specified “whole number,” so I'll accept e and i as solutions. But I do think “alphabetical order” is unambiguous. Reverse alphabetical order is just a different thing.
POTW will return in January! (I haven't figured out the theme yet, though.)
I agree on reverse alphabetical order. I just enjoyed the coincidence that allowing reverse alphabetical order generated all the numbers in Euler's formula as solutions.
Well good luck in Baltimore. If you need any travel health medication such as malaria aid or jet leg treatments, visit https://www.medcare2go.com/treatment/20/travel-health-pharmacy and you will be fine. They ship to your home address. Have a nice trip!
I can think of three answers to the POTW
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