What's so special about 10928094208 in base 77?

One of my current recreational arithmetic side projects is creating a b-file (a longer list of the sequence) for OEIS A281335. 10928094208 is the smallest solution in base 77:

(4,2,67,10,58,31) = 2^10 * 31 * (58,4,67)

The digits of the number (on the left) are matched by the digits of its factorization (on the right). The solution for base 73 is an even bigger number — but I haven't yet figured it out!

Dem dry bones

When I wrote my Weston bones article eleven days ago, I was under the illusion — based on my interpretation of the 1911 newspaper articles — that the find was underneath what was to become Westminster Church School. In a cover story at WestonWeb, a Chris (from the Toronto and Region Conservation Authority) commented that the bones site (AkGv-6) was here; in other words, a little further south. This had me look again at the upper half of the photograph:

There are two buildings in the background and I thought I discerned utility poles in the gap between them. This had to be Main St. — now Weston Rd. Below is a depiction of this part of Weston — a 1910 map (on the left) and a 1913 map (on the right). Main St. runs from upper left to lower right, cutting each map roughly in half.

Yellow structures are made of wood; red, of brick. In the three years between the maps some new buildings have appeared. Some of the wood structures have been replaced with brick. There are also some subtle displacements. In particular, the only two structures below Main St. in 1910 appear on adjacent lots in 1913. I don't think they moved the buildings to make room for the Sunday School (which appears as the big red square). Instead, it seems likely that the 1910 placements were made in error and corrected in the 1913 map. Good thing. You see, I thought those two structures were the buildings in the photograph. But there wasn't enough space between them to account for the gap in the photo. With the 1913 correction, there is now a reasonable window of Main St. (blue arrows) from some location south of the school. And this jives with Chris' placement of the bones site.

Addendum: I've just replaced the maps picture with a new version that has pasted into place (in the 1913 part) two buildings at the end of Hillcrest Rd. that appeared in an adjacent map plate and should therefore have appeared in this one. The newly added brick building now at the bottom of the map appears to be #28 Hillcrest and directories tell me that a Frank Munshaw lived there. Mrs. Munshaw was mentioned in the 1911 Globe article:

Two splendid skulls, however, were rescued from the depredations of the innocent pillagers by Mrs. Frank Munshaw, whose husband is the tenant of the property in which the skeletons were found.

I am now doubting that the two buildings in the photograph are the ones I posited (above). My current best guess is that the L-shaped structure at the bottom of lot P is the building on the left and one of the structures on lot N is the building on the right:

Now hear the word of the Lord!

Lost and found

On December 12 we had our first significant snowfall of the winter. I wrote about it here. Also noted in that post is that I lost my camera's lens cap. I'm happy to report that this morning I found it. There has been an ongoing January thaw (most of the snow is gone) but — as evidenced by the muddy tracks in my photo — I hadn't found the cap sooner because a small excavator (helping lay a new Bell Fibe cable) had been parked atop it.

Easy does it

One thing leads to another. Once I got my library card so that I might access (online) the original newspaper articles for my Weston bones article, I used the tool to go over some family genealogy. I had previously relied on a research associate's access to archived Toronto newspapers for such information but now I was in the driver's seat!

This photo was stolen from here. My wife's grandfather, Frank Powers, had in his obituary that he was a "salesman for the Easy Washing Co. Ltd. for some years". He appears to have had a variety of jobs in his life, including (in the early 1910s) working for a printer and a jeweler. At any rate, I quickly learned that the clothes wringer at the top of the machine was called a mangle. And it would be natural to suppose that this is where the verb to mangle originated. Actually, it was the other way around.

Dem bones

Less than a week ago I started transcribing the 1917 directory of the then-town of Weston, the part of Toronto in which I have resided now for more than fifty years. Proofreading the information (to the extent possible) has led me to look for some streets that are no longer there, which has led me to a remarkable photograph (of which the above is a crop). I'm prepared to believe that putting the boy in there with a shovel was done as a joke. One has to wonder what explanation was given at the time for the presence of these bones.

Glenn Turner (The Toronto Carrying Place, 2015) writes: "So, for some of its distance at least, Weston Road actually may be the Carrying Place. Archaeologist Dr. Shaun Austin believes that the stretch from Wilby Crescent ... to Rectory Road does in fact follow the route of the trail. He bases this on newspaper reports from 1911 of skulls and skeletons being found 'on an old Indian trail'. The burials were part of an ossuary (literally a boneyard, typical of Iroquoian nations like the Wendat and Onondowahgah) located on the site of today's Weston Park Baptist Church, ..." Alas, Weston Park Baptist Church (back then, Alexander Memorial Baptist Church, a small building at the back of today's church) is on the other side of Weston Road from the then-to-be-built (Presbyterian) Westminster Church School (later Westminster United Church, photo 1953; a parking lot, 1957-1970; by 1971, this high-rise), near where these bones were actually found.

An explanation for the (supposedly "men's") bones provided by Barb Shiells, a director of the Weston Historical Society: "Archaeologists advised that the bones were part of a native burial ground and likely dated back to 1425-1450. It was the aboriginal custom, when they were moving on to establish a new village, to hold a sacred ceremony to show respect for their dead. They would gather the previously buried remains and re-inter them in one large pit."

I'm largely unconvinced. For a little perspective, here's what happened on a more recent Toronto "ossuary" find. I've also dug up two newspaper accounts of the 1911 find and one follow-up. I've highlighted the skeletal remains' layout assessments (in blue) contradicted by a supposed expert's assessment (in red) just a few days later. Unbelievable!

30 SKELETONS HAVE BEEN DUG UP AT WESTON
The Toronto Daily Star: Friday, 28 April 1911, page 1

Workmen commencing excavations for the erection of the new Presbyterian Sunday school at the corner of Main and Mill streets, Weston, to-day, came upon over thirty skulls and skeletons at a depth of only two feet from the surface.

The property upon which the interesting relics were found is situated a short distance from the bank of the Humber River, on the old Indian trail running from Lake Simcoe to the place where Toronto now stands, and it is thought by those citizens of Weston who have seen the bones, that they probably indicate the results of an Indian battle fought many years ago.

At any rate, the oldest residents of the town are authority for the statement that the land upon which the shallowly interred remains were discovered, was never used as a white man's burying ground. More bones were turned up hourly as the work went on, and a large crowd of interested spectators lined the street. No decision has as yet been reached as to the disposition of the relics, but it is probable that they will be donated to various museums.

"The general impression in the town seems to be that these are the bones of Indians, thrown in a haphazard way into shallowly dug trenches over half a century ago, and probably long before that," said Rev. Dr. McGillivray, pastor of the Presbyterian Church, for which the Sunday school is being built. "People who have lived here for as long as 50 years can recollect no occurrence which would account for the burial of so many people in such a way."

The bones and skulls are all in a fair state of preservation and were first encountered about fifty feet from the bank of the river. No weapons or other articles that might have explained the matter have been found as yet.

The house which stands on the adjoining lot is 65 years old. The strange thing is that the bones, buried so near the surface, were not discovered long ago. Latterly, the land covering them had been cultivated as a household garden. The property was purchased by the church from a Mr. Hunter of Toronto.

A further examination of the bones and the ground in which they were found may serve to reveal some valuable historic information.

MANY SKELETONS FOUND IN TRENCH
The Globe, Saturday, 29 April 1911, page 9

Bones and skulls comprising fourteen skeletons, possibly of Indians, were dug up by a road-scraper at Weston about 9 o'clock yesterday morning, shortly after excavation had been commenced for the foundation of a new Presbyterian Sunday school hall on the property at the corner of Mill and Main streets. A remarkable fact in connection with the accidental discovery of the skeletons is that they were only eighteen inches below the surface.

The reasons for the conclusion that the bones were those of Indians are many. The Weston road, which runs along beside the scene of the find, was, according to history, formerly an Indian trail. It is also close to the east bank of the Humber River, which in earlier days was navigable for flat-bottomed boats and canoes. An examination of the skulls themselves reveals unmistakable aboriginal anatomical features. Two years ago a skeleton with Indian beads was unearthed just off the main street of Weston, and four or five years ago the skeleton of an Indian chief was found wrapped in a blanket.

Mr. Hector Hart, contractor for the excavation work, told the Globe that while a scraper was at work on a drain being run through the property just acquired by the Presbyterian Church, he noticed some bones in the earth disturbed. The next turn of the scraper unearthed more bones and skulls, and before the ditch was finished fourteen skulls were found. That there is a big trench running parallel with the bank of the river and that the excavation cut at right angles was only a short section of it, and that there are probably scores of skeletons still uncovered, were the views of Mr. Hart and of Rev. A. H. MacGillivray, pastor of the Presbyterian Church.

The spot at which the skeletons were discovered is a few feet back of the church lot and lies in the property of Mr. A. T. Hunter of Hunter & Hunter, barristers, so that Mr. Hunter is the real owner of the aboriginal specimens, although a few curio seekers in town have carried off some of the more complete skulls.

Two splendid skulls, however, were rescued from the depredations of the innocent pillagers by Mrs. Frank Munshaw, whose husband is the tenant of the property in which the skeletons were found.

A large number of persons, mostly curious children, were gathered about the drain throughout the day, and the discovery was the topic of conversation over the entire town.

One resident told a Globe reporter the skeletons was not those of Indians, but the bones of gallant Canadians who fought in the rebellion of 1837 or the war of 1812. He said many lost their lives at Weston during the former trouble and that there were so many fatalities that, instead of burying the bodies in separate graves, the people dug a trench and threw them all in together.

"But," The Globe reporter remonstrated, "Canadians were too highly civilized then to be guilty of such barbarous practices as communal burials."

"Not by any means," retorted the Westonian. "They were not so highly civilized then as you might imagine. And there's a big pile of Canadians to-day no higher up in the ladder of civilization."

The bones and skulls are pretty well preserved and look as if their age should be measured, not by centuries, but by decades or years. An examination of the teeth in some of the jaw-bones shows them to be in a state of perfect preservation. They look sounder than a lot of the teeth being used in 1911 for purposes of mastication.

The skeletons, as an examination of their relative position before being taken from the ground showed, indicated that the bodies at the time of interment were thrown into the trench together without any orderly arrangement, and that the interment probably took place during or just subsequent to hostilities between Indian tribes.

Mr. Hart, who has studied Parkman carefully, stated the Huron Indians originally occupied the vicinity of Weston, but that later the tribes of the eastern States, who were more powerful, drove the Hurons back to Lake Simcoe and Georgian Bay, and that the skeltons found were probably those of the Iroquois or Mohawk Indians.

SAYS SKELETONS CENTURIES OLD
The Globe, Tuesday, 2 May 1911, page 8

Dr. Rowland B. Orr, Superintendent of the Provincial Museum, yesterday afternoon paid a visit to the scene of the unearthing of fourteen skeletons, supposed to be those of Indians, in Weston.

He told The Globe last night after his return that there was no question about their being the skeletons of Indians. The very arrangement of the bones, he says, when they were unearthed was sufficient ground for such a conclusion. He stated that the skulls were close together and that the bones forming the rest of the skeletons lay in such a manner as to form a sort of cart-wheel, with the skulls at the hub. He added that this was the customary mode of burial among the Indians centuries ago and that not only were these Indian skeletons, but they had been there for probably three hundred or more years.

Dr. Orr secured two skulls to take measurements of their various dimensions and also to preserve as curios.

Dem dry bones!

Walter Llewellyn Loyd

When I was doing my releasing-the-stick research I came came across an older version of David Singmaster's Sources in Recreational Mathematics which referenced a newspaper article published shortly after the death of Sam Loyd in which was stated that he was survived by a son and two daughters. Singmaster asked if anyone had ever tracked the daughters and their descendants. Recreational genealogy is one of my hobbies, so I thought I'd give it a try.

It only took a couple of days to collate a decent family tree of the descendants of Isaac Smith Loyd and Elizabeth Singer — all from free web resources and of course a lot of searching. Sam Loyd's son is generally known as Sam Loyd Jr. but as Martin Gardner described it (in Scientific American, August 1957), "when the elder Loyd died, the younger dropped the 'Jr.'".

Photo stolen from this site. Let's do the genealogy:

1873 New Jersey birth registration: Walter L. Loyd
1880 Jersey City NJ census: Walther Lloydd
1892 Brooklyn NY census: Walter L. Loyd
1900 ?  He is not with his parents and younger sister.
1905 Brooklyn NY census: Walter Loyd
1907 Manhattan NY marriage: Walter Samuel Loyd
1908 Manhattan NY birth of his son: Walter Samuel Loyd
1910 Bronx NY census: Samuel Loyd Jr.
1918 Brooklyn NY draft registration: Samuel Loyd
1920 Brooklyn NY census: Samuel Loyd
1930 ?  His wife is back from France a few months after the census. Springer?
1934 Brooklyn NY death: Samuel Loyd

So, we see the general transformation. What happened to the L? Actually, I still found it in use in a 1912 reference (in the 1913 Sam Loyd and his Chess Problems by Alain Campbell White, page 43) where he is L. Sam Loyd Jr. And what does the L stand for? Here I don't have anything definitive but this website suggests that it is Llewellyn (although it erroneously treats it as a surname, thus passing it on to his son).

Finally, I have to pay homage to Alex Jay's profile of Sam Loyd Jr. which anticipated many of my own genealogical points of interest and led me to discover that Emma Agnes Loyd had married.

Releasing the stick

The 1933 "Scarlet River" was playing on Turner Classic Movies between 2 and 3 AM yesterday morning and (for no particular reason) I watched bits of it. What most caught my attention was a sequence where a string-and-stick object was attached to someone's apparel and the unlucky person couldn't figure out how to detach the it. (Some years ago I wrote a handful of puzzles-in-the-movies blogs: I, II, III, IV, V). The Scarlet River puzzle is of course "Releasing the stick" featured in Henry Dudeney's posthumous 1932 "Puzzles and Curious Problems" (#349 therein; it became #530 in the Martin-Gardner-curated 1967 "536 Puzzles & Curious Problems"). It seems reasonable to suppose that the inclusion of the puzzle in the 1933 movie was predicated on the aftereffects of someone having seen it in the 1932 book.

Dudeney wrote: "Here is a puzzle that will often cause a good deal of bewilderment amongst your friends, though it is not so generally known as it deserves to be. I think it was invented by Sam Loyd, the American chess and puzzle genius. At any rate, it was he who first showed it to us more than a quarter of a century ago." I'm not sure when Dudeney wrote that (he died in 1931) but let's agree that the showing was pre-1906.

When Jerry Slocum and Jack Botermans published their "New Book of Puzzles" in 1992, they featured the 1959 "Magic Holetite Pencil" and wrote about its origin:

The famous American puzzle inventor Sam Loyd was asked by the head of the New York Life Insurance Co., John McCall, to make an advertising puzzle that their salesmen could take with them, and that would make their clients remember its message. Loyd went home and returned to McCall the next day with a small stick attached to a loop of green cord. The stick looked like a policeman's billy club and it was slightly longer than the loop. McCall failed to be duly impressed. "What's the purpose of it?" he asked Loyd. Whereupon Loyd took McCall by his lapels, stuck the cord through the buttonhole and the stick in turn through the loop. "Alright," he said, "let's make a bet. If within half an hour, you've gotten the stick out, without cutting the cord, I'll give you one dollar. If not, you owe me one." McCall pulled and pushed and, in short, spent 30 minutes of his valuable time trying in vain to remove the stick. After his time was up, Loyd accepted his dollar with the words: "In return for a $10,000 life insurance policy from NYLI, I'll take the thing right off of you!" Now McCall was impressed. "By this our clients will surely remember our salesmen!" The Buttonhole Puzzle became one of Loyd's most successful puzzles and it created the phrase "to buttonhole" someone.

[Taken from the web; I don't have the book.]

There's a couple of details one gets from this that are at odds with how Alain Campbell White described the events in 1913 (Sam Loyd and his Chess Problems, page 103):

It was Loyd's theory that the simpler a puzzle could be made to appear the more people would try it. It was the same theory that led to his making problems like No. 98, which have become so popular. A good instance is the one which he told about for the Delineator, and which he called John A. McCall's puzzle, after the late President of the New York Life Insurance Co.

"Once John A. McCall sent for me and suggested that I invent something in the puzzle line for his agents to use that would pleasantly keep their mission in folks' minds. The next day I returned with this." Here Loyd drew forth a small stick, some six inches long, cut to represent a toy policeman's billy. It was hung on a green string loop, the loop being almost but not quite as long as the stick. "Well, McCall dangled it on his finger: 'H'm,' said he, 'very neat, but hardly striking, I should say. How do you propose to use it?' I grasped the lapel of his coat, I slipped the string through the buttonhole, and then I pushed the stick so — and then I said, 'Mr. McCall, I'll bet you a hundred dollars to one that you can't get that off in half an hour without cutting the string. McCall put up the money, and so did I, and then he spent thirty minutes of his valuable time tugging at that toy. At the end I pocketed his dollar and remarked, 'Mr. McCall, I'll take that off for you if you'll agree to take out a ten-thousand-dollar policy on your life!' He laughed. 'Great,' he said, 'This'll make folks remember our agents!' That was one of my most successful puzzles."

Slocum and Boterman's addition of the "to buttonhole" origin is pure folk etymology. Sam Loyd died in April 1911. The Delineator mention by White refers perhaps to Walter Prichard Eaton's "Sam Loyd and his Ten Thousand Brain-Teasers" in the April 1911 issue of that magazine (which I wish I had a copy of). At any rate John A. McCall died in early 1906, so anything Loyd said about the origin of the "John A. McCall's puzzle" was thereafter not likely to be challenged. And knowing Loyd's penchant for making self-aggrandizing, bogus claims, I suspect that it was just that!