Tag Archives: Sam Loyd

Butcher Boy Problem

This is another long historical story from Sam Loyd with a puzzle attached.

“NOTICING THE HIGH price recently paid at auction for an autograph of General Grant reminds me to say that I am the proud possessor of what I believe to be the last signature made by General Grant.

The story connected with it introduces a somewhat pretty problem, and induces me to pay a tribute to Grant’s mathematical ability, at the expense of the many who have no love for figures. I take occasion here to say that while journeying through life and jostling up against all manner of people, the fact has been impressed upon my mind that with few exceptions all successful men were those who endowed with a ready faculty for correct mental arithmetic. On the other hand, there is a class of never-do-wells who guess or jump at conclusions in a reckless way, and cannot even figure up how much to pay on the dollar when the inevitable smash comes.

I could mention a dozen incidents connected with great men as illustrating their aptitude for correct calculations, but this one will suffice to call attention to Grant’s aptitude for figures.

We all remember the story of how he figured his way into West Point, after that memorable journey for a pound of butter, when he heard of the chance for a competitive examination. Professor Agnell, the master of mathematics at West Point, with whom I used to play chess, used to say that “Grant had a great love for mathematics and horses.”

Grant did love a horse and could pick out the good qualities at a glance, and, oh, my! how he despised a man who would abuse a dumb animal!

My story turns upon an incident as told by Ike Reed, of the old horse mart of Johnson & Reed, who gave me the autograph from their sales book of 1884, as photographed in the picture. During the last term of his Presidency General Grant returned from his afternoon drive and in a humorous but somewhat mortified way told Colonel Shadwick, who kept the Willard Hotel, that he had been passed on the road by a butcher cart in a way that made his crack team appear to be standing still. He said he would like to know who owned the horse and if it was for sale.

The horse was readily found and purchased from an unsophisticated German for half of what he would have asked had he known the purchaser was the President of the United States. The horse was of light color and was none other than Grant’s favorite horse, “Butcher Boy,” named after the incident mentioned. Well, some years later, after the Wall street catastrophe, which impaired the finances of the Grant family, Butcher Boy and his mate were sent to the auction rooms of Johnson & Reed, and sold for the sum of $493.68. Mr. Reed said he could have gotten twice as much for them if he had been permitted to mention their ownership. But General Grant positively prohibited the fact being made known. “Nevertheless,” said Reed. “you come out two per cent, ahead, for you make 12 per cent, on Butcher Boy and lose 10 per cent, on the other.”

“I suppose that is the way some people would figure it out.” replied the General, but the way he laughed showed that he was better at figures than some people, so I am going to ask our puzzlists to tell me what he got for each horse if he lost 10 per cent on one and made 12 per cent on the other, but cleared 2 per cent on the whole transaction?

It may be mentioned incidentally that General Grant stated that he had presented one of the horses to Mrs. Fred Grant, and as shown in the receipt signed for her.”

See the Butcher Boy Problem

Grandfather Clock Puzzle

This is another doable puzzle from Sam Loyd.

“BACK OF THE OLDTIME song of “Grandfather’s clock was too tall for the shelf, so it stood for ninety years on the floor,” there was a legend of a pestiferous grand-father and a cantankerous old clock which, from the fitful time when “it was bought on the morn, when the old man was born,” it had made his whole life miserable, owing to an incurable habit which the clock had acquired of getting the hands tangled up whenever they attempted to pass.

These semi-occasional stoppages became of more frequent occurrence as advancing age made the old gentleman more irritable and his feeble hands more incapable of correcting the cranky antics of the balky old timepiece.

Once when the hands came together again and stopped the clock the old man flew into such an ungovernable passion that he fell down in a fit, stone dead, and it was then that

“The clock stopped short,

Never to go again,

When the old man died.”

A photograph of the clock was presented to me, showing the classical figure of a female representing time, and it struck me as remarkable that with the knowledge of the hour and minute hands being together that it should be possible to figure out the exact time at which “the old man died,” from the position of the second hand as shown, without having to see the face of the clock. The idea of being able to figure out the exact time of day from seeing the second hand alone is very odd, although not so difficult a puzzle as one would imagine.”

See the Grandfather Clock Puzzle

A Question of Time

This turns out to be an unambiguous, doable problem from the 19th century puzzle master Sam Loyd.  It is based on an observation about jewelers’ signs of the times.  I thought I would include Loyd’s narrative in its entirety.

“A CURIOUS paragraph has been going the rounds of the press which attempts to explain why the signs of the big watches in front of jewelry stores are always alike. They are painted upon the dial, apparently in a haphazard sort of a way, and yet they invariably indicate a certain number of minutes past eight. It cannot be attributable to chance, for it would tax one’s credulity to believe that such a coincidence could occur all over the civilized world.

There is no accepted rule or agreement established with the jewelers or sign painters, for careful inquiry proves that few of them are aware of the fact or ever noticed that any two are alike, it would be a marvelous case of unconscious imitation if it is looked upon as a mere custom, accidentally following a pattern set by the originator of the device of the sign of a big watch. In London, where they take pride in such things, I saw several big watches, looking as if they had hung in front of the stores for countless centuries, all indicating the same mysterious time, accompanied by the announcement that the firms were established a couple of hundred years ago. I do not doubt for a moment that some such similar sign can be found at Nuremberg, where the watch originated during the Fifteenth Century.

The discussion seems to have brought out a recognition of the fact that from an artistic point of view, symmetry requires that the hands should be evenly balanced, as it were, on both sides of the face of the watch.

If they are raised too much there is a certain “exasperating, declamatory effect,” which is not altogether pleasing.

The time would be incorrect if the hands pointed at 9 and 3, and at other points would be too low, so, as a matter of fact, and from an artistic point of view, the position is well selected and is one of the points which, with the aid of a watch, can be shown to be possible. It is a fact however, that the mere puzzle of telling what time the watch indicates, has been held up to public gaze for all these centuries without being thought of or solved?

Take your watch and set it to the time indicated, with the hands at equal distances from the six hour, which shows it to he a possible position, and then tell what time of the day it is! …”

See A Question of Time

Bixley to Quixley Puzzle

I braved another attempt at a Sam Loyd puzzle.

“Here is a pretty problem which I figured out during a ride from Bixley to Quixley astride of a razor-back mule. I asked Don Pedro if my steed had another gait, and he said it had but that it was much slower, so I pursued my journey at the uniform speed as shown in the sketch.

To encourage Don Pedro, who was my chief propelling power, I said we would pass through Pixley, so as to get some liquid refreshments; and from that moment he could think of nothing but Pixley. After we had been traveling for forty minutes I asked how far we had gone, and he replied: “Just half as far as it is to Pixley.”  After creeping along for seven miles more I asked: “How far is it to Quixley?” and he replied as before: “Just half as far as it is to Pixley.”

We arrived at Quixley in another hour, which induces me to ask you to figure out the distance from Bixley to Quixley.”

I was disconcerted by what I thought was extraneous information and wondered if I had misunderstood his narrative again.

See the Bixley to Quixley Puzzle

Tandem Bicycle Puzzle

A glutton for punishment I considered another Sam Loyd puzzle:

“Three men had a tandem and wished to go just forty miles. It could complete the journey with two passengers in one hour, but could not carry the three persons at one time. Well, one who was a good pedestrian, could walk at the rate of a mile in ten minutes; another could walk in fifteen minutes, and the other in twenty. What would be the best possible time in which all three could get to the end of their journey?”

See the Tandem Bicycle Puzzle.

Marching Cadets and Dog Problem

In my search for new problems I came across this one from Martin Gardner:

“A square formation of Army cadets, 50 feet on the side, is marching forward at a constant pace [see Figure]. The company mascot, a small terrier, starts at the center of the rear rank [position A in the illustration], trots forward in a straight line to the center of the front rank [position B], then trots back again in a straight line to the center of the rear. At the instant he returns to position A, the cadets have advanced exactly 50 feet. Assuming that the dog trots at a constant speed and loses no time in turning, how many feet does he travel?”

Gardner gives a follow-up problem that is virtually impossible:

“If you solve this problem, which calls for no more than a knowledge of elementary algebra, you may wish to tackle a much more difficult version proposed by the famous puzzlist Sam Loyd. Instead of moving forward and back through the marching cadets, the mascot trots with constant speed around the outside of the square, keeping as close as possible to the square at all times. (For the problem we assume that he trots along the perimeter of the square.) As before, the formation has marched 50 feet by the time the dog returns to point A. How long is the dog’s path?”

See the Marching Cadets and Dog Problem.