April 2006 - mathfun@mailman.xmission.com

Re: [math-fun] Early Goodbyes
by Jpr2718＠aol.com 05 Apr '06

05 Apr '06

David, Well, I hope you hang around for a long time. Move to southern Florida! That's what I did. Renting a nice apartment is cheap (there's a glut of building), even in the ``fancy'' addresses (Fort Lauderdale, Boca Raton, Delray Beach, West Palm Beach). Everything is flat, so it's easy to get around on a bicycle, and a lot of people do. No snow or ice. Rain is intermittent in the summer and unusual in the winter. There are thousands of valet parking jobs, that pay about $5 per car, and it must be possible to do 40 to 60 cars in a 4 or 5 hour stretch. Because the median age has got to be about 75 around here, there is valet parking not only at restaurants and hotels, but at shopping malls, movie theaters, you name it. If you can afford it, try a career management firm. They are more than placement services, and offer short courses on resume writing, interviewing, and generally how best to present yourself to potential employers and how to find potential employers. Unlike recruiters, they do a whole lot more than send you to random interviews. They'll really hold your hand through the whole process. A really good one in northern NJ is Lee Hecht Harrison, _www.lhh.com_ (http://www.lhh.com) . Or (or and) take a couple of the actuarial exams. Property/casualty insurance is growing and there is a greater and greater demand for quantitative experts of any sort. Sound boring? Currently I'm involved in comparing how much workers compensation costs to treat a given injury versus what it costs in the group health system. It involves taking millions of records for medical transactions and distilling out conclusions that the less technically educated in the industry will find interesting. And doing Bayesian analysis using WinBUGS to forecast all sorts of things of interest in a statistically sound way. In the group I'm in there are 4 of us that have Masters of PhDs from UC Berkeley in math, two Yale PhDs (one in math and one in econ), and two other econ PhDs. There are serious intellectuals outside academia these days. An we don't have to publish or perish (although we have produced some good publications). Branch out. If you can make enough to live on in a 40 to 60 hour week, that leaves a lot of time to pursue hobbies, like math. Hang in there. If for no other reason than to see what happens next. John John Robertson 561-272-0356 jpr2718(a)aol.com

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[math-fun] Two days late
by R. William Gosper 04 Apr '06

04 Apr '06

Chronic anagrammatism leads to irreversible liverberries. Picture this, then look it up: "We sat by a fireplace of foolstones, nibbling angleberries and listening to the Chicago piano." --rwg Puzzle: what is the opposite of Indian Summer? (Hint: not Cowboy Multiplier. California's actually having one.)

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[math-fun] Amusing date
by Steve Rowley 04 Apr '06

04 Apr '06

A colleague points out that tomorrow morning, the time and date will be amusingly symmetrical: 01:02:03 04/05/06. -- Steve Rowley <sgr(a)alum.mit.edu> http://alum.mit.edu/www/sgr/ Skype: sgr000

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[math-fun] Re: Early Goodbyes
by David Wilson 04 Apr '06

04 Apr '06

I can't afford the luxury of hope any more. > What I try to say, is that there's hope even in desperate situations, > and the possibilities > might come from some unexpected avenue. (Of course the situation in U.S. > is in many respects > different. In wich state you live?) > > Have strength, > > Antti

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Re: [math-fun] number of sodoku squares ?
by N. J. A. Sloane 03 Apr '06

03 Apr '06

Henry, If you search under "sudoku" in the OEIS, you will find two relevant entries, as follows. Regards, Neil %I A109741 %S A109741 1,1,2,5472730538 %N A109741 Number of inequivalent (completed) n^2 X n^2 sudokus (or Sudokus). %C A109741 See A107739 for definition of a sudoku. %C A109741 a(2) = 2 independently computed by Gary McGuire and Hugo van der Sanden. %C A109741 For the 9 X 9 case the allowed equivalences are: relabeling entries; reflection; rotation; %C A109741 permutation of blocks of columns 1-3, 4-6 and 7-9; %C A109741 permutation of blocks of rows 1-3, 4-6 and 7-9; %C A109741 permutation of columns 1-3; permutation of rows 1-3; %C A109741 permutation of columns 4-6; permutation of rows 4-6; %C A109741 permutation of columns 7-9; permutation of rows 7-9. %D A109741 J.-P. Delahaye, "Le tsunami du Sudoku" in 'Pour La Science' (French Edition of "Scientific American"), December 2005 pp 144-9, Paris. %H A109741 Bertram Felgenhauer and Frazer Jarvis, <a href="http://www.shef.ac.uk/~pm1afj/sudoku/">There are 6670903752021072936960 Sudoku grids</a> %H A109741 J. P. Grossman, <a href="http://www.mathstat.dal.ca/~jpg/sudoku/">Javascript Sudoku solver</a> %H A109741 Ed Russell and Frazer Jarvis, <a href="http://www.shef.ac.uk/~pm1afj/sudoku/sudgroup.html">There are 5472730538 essentially different Sudoku grids</a> %H A109741 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sudoku">Sudoku</a> %H A109741 S. Gupta, <a href="http://theory.tifr.res.in/~sgupta/sudoku/challenges.html#prime">Exploring the Mathematics of Su Doku</a> %e A109741 a(2) = 2: %e A109741 12|34 12|34 %e A109741 34|12 34|12 %e A109741 --+-- --+-- %e A109741 21|43 23|41 %e A109741 43|21 41|23 %K A109741 nonn %O A109741 0,3 %A A109741 njas, Aug 13 2005 %I A107739 %S A107739 1,1,288,6670903752021072936960 %N A107739 Number of (completed) sudokus (or Sudokus) of size n^2 X n^2. %C A107739 An n^2 X n^2 sudoku is an n^2 X n^2 array which is subdivided into n^2 n X n subarrays. Each row and column of the full array must contain each of the numbers 1 ... n exactly once (this makes it a Latin square of order n). In addition, each of the n^2 n X n subarrays must also contain each of the numbers 1 ... n exactly once. %H A107739 Bertram Felgenhauer and Frazer Jarvis, <a href="http://www.shef.ac.uk/~pm1afj/sudoku/">There are 6670903752021072936960 Sudoku grids</a> %H A107739 J. P. Grossman, <a href="http://www.mathstat.dal.ca/~jpg/sudoku/">Javascript Sudoku solver</a> %H A107739 Ed Pegg Jr, <a href="http://www.maa.org/editorial/mathgames/mathgames_09_05_05.html">Sudoku variations</a> %H A107739 Ed Russell and Frazer Jarvis, <a href="http://www.shef.ac.uk/~pm1afj/sudoku/sudgroup.html">There are 5472730538 essentially different Sudoku grids</a> %H A107739 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sudoku">Sudoku</a> %e A107739 Comment from Hugo van der Sanden (hv(AT)crypt.org) Jun 12 2005: "Consider n=2: renumbering doesn't affect the result, so we can fix row A at (1, 2, 3, 4) and multiply the result by 4!. Once rows B and C are chosen, there is only one option for row D. Row B must have (3, 4) or (4, 3) followed by (1, 2) or (2, 1). %e A107739 "Rows C and D can be swapped without affecting validity, so we can fix column 1 of row C to be the lower of the two options and multiply the results by 2. %e A107739 "That leaves at most 4 options for row C (2 choices in each of the remaining 3 positions, of which one must have our selected number as one of the choices); that leaves 16 options to check for rows B and C, the result to be multiplied by 48. %e A107739 "Checking, we find just 6 of the 16 grids are valid: %e A107739 1234/3412/2143/4321 1234/3412/2341/4123 1234/3421/2143/4312 %e A107739 1234/4312/2143/3421 1234/4321/2143/3412 1234/4321/2413/3142 %e A107739 so a(2) = 6 * 48 = 288." %e A107739 An example of a sudoku of size 9 X 9: %e A107739 124|567|893 %e A107739 378|294|516 %e A107739 659|831|742 %e A107739 ---+---+--- %e A107739 987|123|465 %e A107739 231|456|978 %e A107739 546|789|321 %e A107739 ---+---+--- %e A107739 863|972|154 %e A107739 495|618|237 %e A107739 712|345|689 %Y A107739 Cf. A109741. %K A107739 nonn,bref %O A107739 0,3 %A A107739 Richard McNair (rmcnair(AT)ntlworld.com) Jun 11 2005 %E A107739 Entry revised by njas, Aug 12 2005

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[math-fun] moderator outage; math undergrad rec?
by Schroeppel, Richard 02 Apr '06

02 Apr '06

I'll be away for a week. Play nice. ---- A daughter of a family friend is about to select her college. She likes math, so I want to recommend some good undergraduate math programs. My own experience is 40 years out of date. Back then, MIT provided an excellent undergrad math program, in spite of their overall neglect of undergrads, and a sink-or-swim attitude. (Maybe I should rephrase that to "the survivors got a good math education".) Anyway, I'd like some more up to date information. Rich

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[math-fun] some neat products
by Joerg Arndt 02 Apr '06

02 Apr '06

At http://arxiv.org/abs/math/0401406 Jonathan Sondow gives products for e^gamma, pi/2 and e All of them of the form \prod{{F_n}^{e_n}} where F_i=\prod_{k=0}^{n}{ (k+1)^{ (-1)^{k+1}\binomial{n}{k} } } Just the exponents e_n are different. -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.

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[math-fun] number of sodoku squares ?
by Henry Baker 01 Apr '06

01 Apr '06

Forgive me if I missed this in the previous sodoku discussion, but how many "essentially inequivalent" such (completely filled in) squares are there? By "essentially inequivalent", I mean modulo the following symmetries: 1. the group of rotations & flips of the entire square. 2. the symmetries of exchanging rows & columns. Exchanging entire 3x3 blocks gives 3!; exchanging rows & columns within blocks gives (3!)*(3!)*(3!). 3. relabelling of the integers from 1-9. So if "1" becomes "9" and "9" becomes "1", they are the "same" square. After all of these symmetries, I would imagine that there could only be a handful of inequivalent squares -- perhaps only one?

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Re: [math-fun] Pandiagonal Sudoku?
by Sterten＠aol.com 01 Apr '06

01 Apr '06

In einer eMail vom 01.04.2006 09:50:26 Westeuropäische Sommerzeit schreibt cboyer(a)club-internet.fr: April 2006 issue, page 70, of Mathematics Today (IMA, the Institute of Mathematics and its Applications, UK). In the same issue, the second part of the article on pandiagonal magic squares published by Dame Kathleen Ollerenshaw. is it available online somewhere ?

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[math-fun] Pandiagonal Sudoku?
by Christian Boyer 01 Apr '06

01 Apr '06

Do you know if a pandiagonal Sudoku has already been published? I have a 25x25 example, the smallest possible size for this problem, but perhaps the same work has already been done. "Pandiagonal Sudoku" means that all the diagonals and broken diagonals of the square should also contains all the numbers, as it is for rows, columns, and sub-squares. It is proved that a pandiagonal Latin square cannot exist for 2k and 3k orders, meaning that a pandiagonal Sudoku of standard size (9x9) is impossible. I know published 25x25 pandiagonal Latin squares, but they are not Sudokus, because they are not organized in 5x5 sub-squares. Christian.

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