August 2020 - mathfun@mailman.xmission.com

Re: [math-fun] MoMath's Mindbenders for the Quarantined
by Dan Asimov 26 Aug '20

26 Aug '20

There's no reason anyone should have to "sign up" when MoMath could easily just post the problems on their website. I suspect they just want a bunch of people they can hit up for money. Peter Winkler has written at least two books of mathy puzzles, which I own. Can it be that these puzzles are from those? Could you (Mike) post a few of the best ones to math-fun? —Dan ----- I think MoMath’s weekly puzzle series hasn’t been mentioned on math-fun. In case you want a nice weekly puzzle, consider subscribing (it’s free). They range from numerical, to logical, to somewhat geometric. None require any math beyond algebra, and they each involve some kind of “aha!” insight, explained in the solution sent 6 days later. -----

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Re: [math-fun] Another Lex. Earliest Sequence: Scott Shannon's "Enots Wolley sequence A336957
by Neil Sloane 26 Aug '20

26 Aug '20

if a(4) = 9 then a(5) does not exist. therefore a(4) > 9 Best regards Neil Neil J. A. Sloane, President, OEIS Foundation. 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane(a)gmail.com On Tue, Aug 18, 2020 at 2:47 AM Frank Stevenson < frankstevensonmobile(a)gmail.com> wrote: > Hi Niel, > > I was trying to compute this sequence, but I am having problems > understanding the concept of lexicographical earliest. Why is not 9 the 4th > number in the sequence, but 15 is ? Why not 105, 1005, 100005 etc ? What am > I missing ? > > Regards, > Frank > > > On Sun, Aug 16, 2020 at 5:56 AM Neil Sloane <njasloane(a)gmail.com> wrote: > >> Obviously this is an inverted version of the Yellowstone sequence A098550 >> ! >> The name Enots Wolley is for personal use only, it must not be mentioned >> in >> the OEIS! We frown on such made-up names. >> >> Definition: Lexicographically earliest sequence {a(n)} of distinct >> positive >> numbers such that, for n>2, a(n) has a common factor with a(n-1) but not >> with a(n-2). >> 1, 2, 6, 15, 35, 14, 12, 33, 55, 10, 18, 21, 77, 22, 20, 45, 39, 26, 28, >> 63, ... >> The original idea was due to Scott, with a different sequence, but this is >> my (canonical!) version. >> >> Could someone please prove the conjecture that this is a permutation of >> the >> set {1, all numbers with at least two distinct prime factors} ? >> >> I can't even prove that every number 2*p (p prime) appears, or that there >> are infinitely many even terms (although I've found a dozen false proofs). >> It's a slippery problem. >> >> Neil >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >> >

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[math-fun] MoMath's Mindbenders for the Quarantined
by Mike Beeler 26 Aug '20

26 Aug '20

I think MoMath’s weekly puzzle series hasn’t been mentioned on math-fun. In case you want a nice weekly puzzle, consider subscribing (it’s free). They range from numerical, to logical, to somewhat geometric. None require any math beyond algebra, and they each involve some kind of “aha!” insight, explained in the solution sent 6 days later. Last night they had a “Best of Mindbenders” meeting via Zoom. People voted for their most favorite, least favorite, hardest, and most poorly defined puzzle. There have been 23 puzzles so far, and Peter Winkler thinks he has enough more to last until the pandemic is over. The MoMath lady who introduced the meeting said they have 9500 subscribers in many different countries. These puzzles are probably back-of-the-envelope (if not do-in-your-sleep) for math-funsters, but many have generalizations that are non trivial. — Mike > Begin forwarded message: > > From: "National Museum of Mathematics" <functions(a)momath.org <mailto:functions@momath.org>> > Subject: Mind-Benders for the Quarantined! > Date: March 20, 2020 at 12:03:01 PM EDT > To: "Mr. Mike Beeler" <mikebeeler2(a)gmail.com <mailto:mikebeeler2@gmail.com>> > Reply-To: "National Museum of Mathematics" <functions(a)momath.org <mailto:functions@momath.org>> > > Dear MoMath friends, > MoMath is pleased to announce a new program to keep your minds fresh! Sign up now for Mind-Benders for the Quarantined! at mindbenders.momath.org <https://momath.org/wp-content/plugins/civicrm/civicrm/extern/url.php?u=2427…> and each Sunday, MoMath will send you a challenging mathematical puzzle from the collection of our own puzzle master, Dr. Peter Winkler. On Tuesday, you'll receive a subtle hint; on Thursday, a serious push; on Saturday, the solution. And the next day, of course, a new puzzle. > These puzzles are for your edification, enjoyment, and personal satisfaction. If you wish, however, you may send your answers and/or complaints to mindbenders(a)momath.org <https://momath.org/wp-content/plugins/civicrm/civicrm/extern/url.php?u=2428…> at any time. Dr. Winkler won't be able to reply, but he will be happy to benefit from your comments, and will announce a winner (for the most right answers with the least help) when the epidemic is over. > Regards, > National Museum of Mathematics > > Support MoMath at momath.org/contribute <https://momath.org/wp-content/plugins/civicrm/civicrm/extern/url.php?u=2429…> > momath.org <https://momath.org/wp-content/plugins/civicrm/civicrm/extern/url.php?u=2430…> > 212-542-0566 > 11 E 26th St > New York, NY 10010 > United States

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[math-fun] Combinatorics of shell substitution
by Robin Houston 25 Aug '20

25 Aug '20

I posted the below puzzle to Twitter, where no one has solved it. I think it’s too hard. Although it’s a silly question, the method of solution is quite interesting IMHO. (The computation would be doable by hand, if one were patient and careful, but can be done more easily and reliably by a computer.) I know some of you are aware of a related problem I solved a few years ago. The method of solution of this one is related, but not identical. Cheers, Robin A Unix shell puzzle. If you were to run this script – which I don’t recommend doing – how many occurrences of $x would appear in the output? x=\"\'\$x\'\"\$x\'\"\$x\"\' eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x eval x=$x echo "$x"

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Re: [math-fun] Legendary Chalk
by Dan Asimov 25 Aug '20

25 Aug '20

The article, with lines like ----- How did a brand of chalk develop a cult-like following? ----- seems to be fact-free. (I always used to buy An-Du-Septic dustless chalk, which worked just fine. <https://shop.crayola.com/color-and-draw/an-du-septic-anti-dust-chalk-sticks…>.) I'm happy to use chalk on a blackboard or markers on a whiteboard, both of which seem to have gone out of style in favor of overhead or PowerPoint-type presentations. —Dan Hilarie Orman wrote: ----- Does anyone really use chalk anymore? If so, is Hagoromo really this good? https://www.cnn.com/2020/08/22/us/hagoromo-chalk-great-big-story-trnd/index… -----

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[math-fun] Legendary Chalk
by Hilarie Orman 25 Aug '20

25 Aug '20

Does anyone really use chalk anymore? If so, is Hagoromo really this good? https://www.cnn.com/2020/08/22/us/hagoromo-chalk-great-big-story-trnd/index… Hilarie

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[math-fun] A variant of the muffin problem
by James Propp 25 Aug '20

25 Aug '20

>From https://mathenchant.wordpress.com/2020/08/16/the-muffin-curse/ (slightly adapted): Imagine an infinite supply of 1-ounce chocolates rolling off an assembly line that's staffed by two immortal and indefatigable employees (call them Ethel and Lucy) who have to feed an infinite line of students. When a new chocolate arrives, Ethel cuts it up and puts pieces into an infinitely large holding area; meanwhile, Lucy takes pieces from the holding area and hands them out to students. All the chocolate pieces must be handed out to students, and each student must get exactly *x* ounces of chocolate. If Lucy and Ethel want the smallest piece any student gets to be as large as possible, what goal should they shoot for, as a function of *x*? I'm pretty sure that when *x* is rational, this is just the muffin problem discussed in this forum back in 2008. But what happens when *x* is irrational? If, say, *x* is the golden ratio ϕ = (1 + sqrt(5))/2 = 1.618..., is there a way for Ethel to divide the 1-ounce chocolates into smaller morsels, and for Lucy to distribute the morsels, so that every morsel gets eaten, and every student gets exactly ϕ ounces of chocolate, and no morsel is less than 0.4 ounces? It may be relevant to mention that for the original muffin problem, f(m,s) (defined as the maximum possible size of the smallest piece among all ways of distributing m muffins among s students) has the property that f(m,s) = g(m/s) for a certain function g that is NOT continuous as a function from the rationals to the rationals (here I am using the epsilon-delta definition of continuity, which makes sense even when the domain of a function is the rationals). So g(.) does not admit an extension to an everywhere-continuous function from the reals to itself (in case you were hoping, as I was, that this would be the answer). There may be some sort of semicontinuous extension at work here. I chose 0.4 because if we let s and m be consecutive Fibonacci numbers, then g(m/s) seems to be converging to something slightly larger than 0.4. Here's Richard Chatwin's article: Richard Chatwin, An optimal solution for the muffin problem, https://arxiv.org/pdf/1907.08726.pdf. Jim Propp

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[math-fun] Another variant of the muffin problem
by Dan Asimov 25 Aug '20

25 Aug '20

Define N(m,s) as *the minimum number of pieces* necessary to distribute m/s muffins to each of s students, starting from m whole muffins. Is N(m,s) easy to determine? —Dan Jim Propp wrote: ----- ... the original muffin problem, f(m,s) (defined as the maximum possible size of the smallest piece among all ways of distributing m muffins among s students) ... -----

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[math-fun] A fractal spiral?
by Éric Angelini 25 Aug '20

25 Aug '20

Hello Math-Fun, (a few friends in copy) this is in French — but easy to understand with the illustrations. In short: 1. seq D 2. digits of D form seq S 3. seq S is turned (on a 2D square grid) into a single-digits spiral 4. This spiral is fractal: its odd digits reshape the spiral itself (the digits have a peculiar design) ... This idea came to me after a discussion on SeqFan about the precise (and seemingly impossible) definition of the term « fractal ». This was submitted this morning to the French magazine Tangente: https://cinquantesignes.blogspot.com/2020/08/partir-en-recursion.html?m=1 Best, É. Catapulté de mon aPhone

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[math-fun] Meeting time
by Kelly DeRango 24 Aug '20

24 Aug '20

Hi Rich: I hope your conference went well last week. We would love to schedule a time for you to speak to our math club. School is beginning this week in Michigan and so I am either teaching or in meetings until 3:30 pm eastern time M-Th and until 2:45 pm on Friday. I am available after those times. Right now we have a Math Club virtual meeting set up for 3 pm Friday. Let me know if you can make a meeting sometime this week, it wouldn't have to be the Friday meeting we have set up but could be if that is what you prefer. Stay safe! Kelly -- Kelly DeRango Battle Creek Area Math and Science Center -- ------------------------------------------------------------------------------------------------------ This email is intended only for the use of the addressee(s) named herein. It may contain legally privileged and confidential information. If you are not the intended recipient, or an authorized representative of the intended recipient, you are hereby notified that any review, copying or distribution of this email and its attachments, if any, is strictly prohibited. If you have received this email in error, please immediately notify the sender by return email and delete this email from your system. Thank you.

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