Emmo W.

Emmo W. was the nom de plume (by way of M.O.W.) of a Melvin Oscar Wellman. Melvin was born 18 January 1881 in the township of Danby, Michigan (roughly west-northwest of Lansing). In 1910 we find him in Charlotte with a wife and two sons; and from 1920 on, in Lansing.

I am indebted to Melvin's grandson, William W. Wellman, for providing me with additional information. He writes:

I spent a lot of time fishing with my grandfather, into my mid-teens. Melvin was an avid fisherman who made split bamboo fly rods, for himself and both of his sons. Every summer in the early 1900s, he took his family by rail to Petoskey, Michigan to spend weekends fishing local small lakes accessible by train. During the week, he barbered in a popular barber shop, McCarthy's, where he may have cut Ernest Hemmingway's hair.

Melvin was the inventor of several camping products but never applied for patents. He used an early hearing aid and founded the Michigan Better Hearing Association, now known as the Michigan Speech-Language-Hearing Association.

Even though my grandfather only had an 8th grade formal education, he was the smartest person I ever knew. He was an avid reader of English, history, and puzzle books. 

Melvin was also a regular contributor in the 1940s to The Enigma (a publication of the U.S. National Puzzlers' League) and is credited with introducing therein, in March 1945, the spoonergram. In the April 1948 issue, he gave us this enigma:

And here is how the mysterious Dr. Matrix (Martin Gardner narrating) paraphrased it in Scientific American in January 1960 (page 154):

"11 plus 2 minus 1 is 12. Let me show you how this works out with letters." He moved to the blackboard and chalked on it the word ELEVEN. He added TWO to make ELEVEN-TWO, then he erased the letters of ONE, leaving ELEVTW. "Rearrange those six letters," he said, "and they spell TWELVE."

The anagram ELEVEN + TWO = TWELVE + ONE is well known in word-play circles, though generally stated without attribution. Now you know from whence it came.

Here is a photo of Melvin and his wife Lucy, later in life. Melvin died 7 October 1955.

Manhunt marathon

When (this evening) I finally sat down to watch television (instead of just listening to it from my computer room), I augmented CNN with a Google+ feed of #Watertown on my iPad. When someone posted that the suspect was in a boat, I took it for a troll (a little contextual information would have helped) — until CNN reported it as well, some minutes later. News of the capture, likewise, preceded CNN's reporting of it by four or five minutes. Of course it is difficult to ascertain which posts offer credible information but as long as one maintains one's usual sense of skepticism, a several minutes advantage in an unfolding news event is manhunt manna.

How far apart were the two Boston marathon bombing sites?

"50 to 100 yards" according to Boston Police Commissioner Ed Davis in a news conference. A lot of newspapers printed this as though it might be true. Canadian media settled on 100 meters as a good-enough approximation. I was pleasantly surprised that Wikipedia (when I checked earlier today) had the blasts occurring "within 550 feet" of each other — somewhat closer to the truth.

The blast locations are no secret: There are plenty of photographs. The first happened in front of Lens Crafters at 699 Boylston; the second, in front of Forum at 755 Boylston. Some folk tried to place the first blast in front of Marathon Sports, next-door to Lens Crafters, but the damage done to the Lens Crafters facade speaks for itself.

So we know each location within a meter or two. Using Google street view to familiarize oneself with the street and building appearances, one can — in Google Earth — situate correctly both locations using the ruler tool: 183 meters, give or take.

Composition

Primes, primes, every where,
Was all the bard did think;
Primes, primes, every where,
But nary one in link.*

This base-ten sequence exhibits an absence of prime linked primes (that is, the concatenation of any number of consecutive terms) in an infinite sea of primes:

2, 5, 11, 13, 29, 31, 17, 19, 43, 7, 37, 41, 71, 47, 67, 89, 3, 101, 23, 109, 59, 83, 103, 73, 107, 157, 53, 127, 149, 61, 131, 139, 79, 163, 191, 193, 97, 113, 137, 167, 211, 181, ...

Such sequences are not rare, this one being the lexicographically first. Here is the base-two analogue:

2, 5, 17, 13, 11, 23, 3, 19, 7, 53, 37, 31, 47, 29, 43, 59, 41, 73, 67, 83, 89, 61, 79, 71, 107, 97, 127, 131, 101, 113, 151, 103, 137, 109, 167, 179, 139, 227, 149, 191, 157, 193, ...

Here is one that works in either base-two or base-ten:

2, 5, 17, 43, 7, 23, 19, 127, 11, 41, 157, 101, 13, 131, 3, 211, 37, 149, 163, 173, 31, 107, 229, 29, 89, 67, 109, 223, 73, 193, 47, 79, 59, 71, 179, 191, 151, 97, 269, 139, 277, 227, ...

And this one works in any base from two to ten:

2, 229, 131, 263, 37, 421, 491, 223, 911, 127, 167, 383, 1187, 401, 31, 15307, 701, 971, 2797, 3, 8741, 571, 5477, 6037, 619, 859, 6359, 353, 2659, 311, 3851, 379, 7193, 7993, 3319, 653, 691, 13441, 661, 1579, 7541, 1987, ...

* Primes of the Ancient Mariner

Hoffman's packing puzzle

This is a photo of my Bill Cutler version of Hoffman's packing puzzle which I have had socked away in a cabinet for the better part of thirty-five years. The blocks are 15x18x22 deci-inches and the frame, 55 cubed. Bill's pieces (each one composed of a 7.5x18x22 doublet) sport some rough saw-cut ends and sides. The frame was originally a box, but one of its sides warped and I decided that it would look better with that and another one of its sides removed. Fine woodworking versions have been created by Trevor Wood and John Devost. Gemani Games and Puzzles sells a version in Samanea.

Dean Hoffman thought up the packing problem in 1978 (Bill Cutler thinks it was 1976: see #8 here) and wrote about it in David Klarner's The Mathematical Gardner (1981, pages 212-225). Elwyn Berlekamp, John Conway, and Richard Guy covered it in their Winning Ways (1982, volume 2: pages 739-740, 804-806; 2004 second edition, volume 4: pages 847-848, 913-915). Alexey Spiridonov published a very nice article about it and its solutions in 2003 and posited an approach to solving the four-dimensional analogue. I don't know if this has yet been accomplished. George Miller, on one of his Puzzle Palace pages, has Donald Knuth searching (in 2004) for solutions to a 3x4x5 version of Hoffman's problem and finding three where one could squeeze an extra 28th block into a 12-cubed frame!

Coming out

The stove is in, Hazel's pen has been rebooted, and she has been let out to scamper around the new floor and get reacquainted with the furniture. Sharing a kitchen with a rabbit might not be everyone's cup of tea but it is manageable and allows us to spend more time with her than we might otherwise.

Also, the kitchen opens onto our back deck and I have been known to let Hazel out occasionally to enjoy the great outdoors. Catherine is disinclined to do so, put off by the incessant self-scratching behavior of our rodent visitors.

First light

Our kitchen makeover involved painting the walls, laying down a new floor, and installing a new stove. Here is Catherine lighting it. It still needs to be pushed back into its space between the cabinets but we will wait for help so as not to scratch the floor.

The oven part of our previous stove had not been used in a very long time because, many years ago, mice had gotten into it and made it their abode. Catherine has been using a mini-oven to do her baking since but I have not done any baking at all, which is a shame because I used to make some decent cakes. I will have to bake one for Catherine's upcoming birthday!

A mathematically crippling deformity

I've written about Stewart Coffin's Convolution puzzle before. John Rausch has a partially assembled Convolution on his Puzzle World website, to which I have added x,y,z axes and red line that goes from (2,2,2) to (2,2,3):

Three pieces (F, D, and G) need to be added to the assemblage. The black cubies end up in the corners of the finished cube. Also, F and G are seriously foreshortened (what look like one-cubie extensions going to the back are actually two-cubie extensions). The number of cubies in each of the three unassembled pieces is 9 (to fit into the 27 empty spaces of the unfinished cube). Can you complete the construction in your head?


I'm going to describe in some detail the 'rotation' that makes Convolution such an interesting puzzle. Bill Cutler once told me that he had done the math, but any mention of the rotation today (as far as I know) neglects to provide any details beyond pointing out that one or more cubie edges are slightly rounded to allow it.

It is D that is the next piece to get added to the unfinished assemblage. Because there is some degree of freedom in how initially this happens, I will describe instead the reverse process: how D is removed from an assembled cube where G and F (in that order) have already been removed. In its final resting place, D's black cubie will sit at the (0,4,4) corner of the finished cube. The other end of D (the final cubie of the three-cubie straight arm) will sit underneath the black cubie whose corner is at (4,0,4). How it got there is of course what this blog entry is all about.

All the action happens in a space parallel to the xy plane (from z=2 to z=4). To dislodge D, first it is pushed down the y-axis by one unit. Having done so, the view of D from above the xy plane will be:

I've added a grid at z=4 showing a few coordinates and two points: A at (2,1) and B at (3,2). Now, the 'rotation': What happens is that A slides along y=1 toward the right while, at the same time, B slides along x=3 toward the top. How long is the slide? Somewhere between D's x=3 line reaching the point (4,1) and D's (4,2) corner reaching the line y=3. Within this range, piece D may be removed by lifting it up the z-axis.

What happens to the line (2,2)-(2,3) during this movement? It slightly ablates the upper-right quadrant at (2,2), though not of course at that level (because the cubies are connected) but, rather, at the level below: The (2,2,2)-(2,3,2)-(2,3,3)-(2,2,3) face of the lower-level cubie in my prior-to-rotation picture will ablate the red-line edge previously noted in the John Rausch picture.

Is this the only edge that is compromised? Convolution designer Stewart Coffin said that the assembly "requires a rotation, which is not possible unless certain edges are rounded ever so slightly". [The Puzzling World of Polyhedral Dissections, 1990, page 52; or here]. So he implies more than one. But this may have been a woodworking — not a mathematical — depiction. Once the (red) edge has been rounded, it allows the rotation/slide to proceed slightly before the one-unit push down the y-axis is fully complete, but at the expense of the lower-level B-point edge on the D piece.

In that 1990 reference, Coffin asks: "Can any reader devise a way to correct this mechanically slight but mathematically crippling deformity in an otherwise satisfactory design?" I discovered this week that such an improvement exists.

Eight- and nine-letter words in base-26 pi: II

The 32 eight- and nine-letter words from Peter Norvig's Google word-count file that were found in half a billion letters of the base-26 π-code representation of the real digits of π have now been supplemented by finds from larger data sets (not restricted by Norvig's at-least-100000-mentions cutoff criterion).

Specifically, my search resulted in an additional 55 eight-letter and 9 nine-letter hits. Of the eight-letter finds, I decided to reject goyetian, rosaruby, avanious, fleyland, commoney, scambler, and tortuose. I immediately recognized the nine-letter beakerman as a word I had come across in December 2003 (at the time, I had saved a picture of muppet Beaker and had given it that name) but I have no corresponding Mathematica notebook to document the find and have only a vague recollection of extending my year-2000 calculation. At any rate, I had struggled back then with recognizing beakerman as a legitimate word and I did so again now. (I have kept it.) So, 32+55-7+9 = 89 words:

  3095146  Armagnac
  5204508  reformist
  5446573  fabledom
 12767754  pediatry
 23893131  keratoma
 26460749  plastics
 30620629  Batavian
 34355657  sailorly
 38729316  hatbrush
 46803099  Gemmingia
 49292523  raisonné
 52221111  beakerman
 52374041  infandous
 62288036  Altamont
 68386037  handsome
 77174448  piquance
 80344659  spraints
 85983887  ticktock
 95489940  freewill
104799581  glassful
119398927  obligate
122636295  derriere
144023162  tarragon
145410250  Pannonic
148864411  aphicide
160285943  conveyer
168667826  hockshin
179537813  caraboid
186970055  lineages
194941942  symbolic
203750087  drawling
204682494  subreguli
213927339  aquiform
220130527  pajamaed
223387624  blurbist
227698058  Gederite
232625291  moromancy
233706360  Brockway
238312955  homicide
241593178  aularian
244832756  coenzyme
245790734  clinamen
248977229  offenses
253217633  somewise
258077020  masslike
265316858  draftily
270498733  puncheon
290930240  friction
291953969  Judentum
296560665  torpidity
298503676  eddyroot
308820127  engaging
309864510  octapody
310692296  Alabaman
317941229  outgrown
324802306  dartlike
326873656  hayfield
327954809  jamboree
330311394  grubbily
331195875  monodont
334661344  venially
339119974  panderly
341079873  magneton
358147952  benzamide
362326813  autopsic
378333440  bookings
379470966  assenter
400726498  cardanic
414326761  immotive
426642188  slubbery
428186515  noblesse
433412589  inertial
440674037  ephebeum
442091394  unkilled
443277601  bioplasm
444201817  Crataeva
452027527  driftlet
454659011  pineland
460082749  loathness
467631243  prickish
468685858  pyroboric
475910828  Mersenne
476984745  stigmatic
479595795  Vallarta
480168788  sunblink
483460192  atmiatry
487934346  copyists
488079020  Assyrian
499784890  southron

A ten-letter word is not found in this range — unless we are willing to allow backwords:

..rlivetumsnwlieeqremonobonseetacejbfepewqxd..

At index 115577805 is the string remonobons, which is snobonomer in reverse. William Makepeace Thackeray used this word in his satirical writing: "Some telescopic philosopher will arise one day, some great Snobonomer, to find the laws of the great science which we are now merely playing with, and to define, and settle, and classify that which is at present but vague theory, and loose, though elegant assertion."

Eight- and nine-letter words in base-26 pi

In my previous post, I provided some English number words that appear in Mike Keith's base-26 π-code representation of the real digits of π. This entry is about other words.

In 2000, I found the eight-letter armagnac at index 3095146. Now, with half a billion strung-together letters (one hundred times the "real estate") at my disposal, I expected to find many more eight-letter words and, hopefully, some larger ones as well. I used eight- and nine-letter words culled from Peter Norvig's Google word-count file made available in his recent English Letter Frequency Counts essay.

A search resulted in 35 eight-letter and 2 nine-letter hits. I dismissed gruening, schreber, brentano, and hillquit for being surnames only. (I kept mersenne because of its adjectival usefulness in mathematics.) I also excluded thoufand — an alternate, incorrect version of thousand resulting from the difficulty of distinguishing a long s from an f in old-English typography. That thoufand had 158819 mentions in Norvig's data set amply demonstrates his list's limitations (and questions his conclusions).

In the following, I have capitalized the words (including a German one) that I felt needed capitalization and added an accent on one of the three French words.

  3095146  Armagnac
  5204508  reformist
 26460749  plastics
 30620629  Batavian
 49292523  raisonné
 62288036  Altamont
 68386037  handsome
 95489940  freewill
119398927  obligate
122636295  derriere
144023162  tarragon
160285943  conveyer
186970055  lineages
194941942  symbolic
203750087  drawling
233706360  Brockway
238312955  homicide
244832756  coenzyme
248977229  offenses
290930240  friction
291953969  Judentum
308820127  engaging
317941229  outgrown
327954809  jamboree
378333440  bookings
428186515  noblesse
433412589  inertial
475910828  Mersenne
476984745  stigmatic
479595795  Vallarta
487934346  copyists
488079020  Assyrian

32 words: It's a start.