88 



♦ KNO^A^LKDGE ♦ 



[February 1, 1887. 



ONE-SCALE ATLAS. 



MAP No. II. is unavoidably postponed till next month. 



THE FIFTEEN SCHOOLGIRLS' PUZZLE. 



E have received from Mr. (Jarpmael a very 

 full ditscussion of this problem, as dealt with 

 by him in the proceedings of the Mathe- 

 matical Society. For the present, howevei', 

 we can only find space for the following 

 suggestive comments by " Mogul " : 



I note that you omit all reference to a 

 mode of solving the schoolgirls' puzzle on 

 quite diJferent ]irinci]iles to any of those referred to in your 

 last article, and which mode may be thus described : 



Describing the girls by the numbers 1 to 

 15 instead of by letters ; thus let 1 remain 

 in the same place all the 7 days, then 

 arrange the remaining 1 4 in two series of 7 

 each, so that on ea-ch succeeding day evei'y 

 number shall occupy the place occupied the 

 day before by the next numbei- in the 

 series — e.g. suppose one series commenced 

 2, 10, 13, itc, then 2 would always go 

 where 10 was the preceding day, and the 10 be moved on to 

 where the 13 was, itc. It does not i-equir'e much considera- 

 tion to .show that one of the series will commence with 2 

 and the other with 3, so that each of these numbers may on 

 every seventh daj' revert to the first row, and not come into 

 it till then. The difliculty consists in airanging the other 

 numbers so that in the isolation of the two series no two 

 numbers who have ever once nwt shall ever meet again. 

 One solution on this pilneiple — for there ai'e many of them — 

 is as under : 



(1) 1 2 3 (2) 1 14 7 



4 5 6 15 11 8 



7 8 9 5 3 12 



10 11 12 6 10 2 



13 14 15 4 13 9 



(5) 1 15 10 (6) 1 9 6 



2 8 5 U 3 11 



6 11 13 .s 1(1 4 



7 3 4 5 7 15 

 12 9 14 2 12 13 



(3) 1 13 5 



9 10 3 



117 2 



8 6 14 



15 4 12 



(4) 1 4 11 



12 6 7 



10 5 14 



3 S 13 



9 15 2 



(7) 1 12 8 (8) 1 2 3 



13 7 10 4 5 6 

 3 6 15 7 8 9 



11 5 9 10 11 12 



14 2 4 13 14 15 



11 



The si.xteen whist-players can easily be solved in the 

 way. One solution is : 



These series are found out partly by lule and partly ten- 

 tatively. Where the numbers run high, the tentative part 

 admits of so many variations that it is very difficult to hit 

 on the right one; and I must confess that though I have 

 almost hit upon two series of 10 each to solve the puzzle of 

 the 21 girls going out for 10 consecutive days in 7 rows of 3 

 each without any 2 ever meeting twice in the second row, I 

 liave not yet quite sucL-eeded. I wonder whether Mr. East 

 Mar.sden, who in your number for March 23, 1883, gave 

 such a very clever solution of this very puzzle, could find 

 out the two series; for I am convinced they must exist. 



"Mogul" also sends a solution of the problem of 16 

 whist-players by the method we followed. 



ASTRONOMY AT OUR EDITOR'S AMERICAN 

 HOME. 



HE following i>aper, while allowing readers 

 of Knowledoe to congratulate themselves 

 on the potent influence which their faithful 

 editor has been able to exert (foi- we must 

 believe everything read in the newspapers) 

 iin the progress of astronomy in Western 

 America, will also serve at once to give a 

 good example of American ncw.spaper jocularity and of the 

 use of particular phrases in the land of the free — and easy. 

 It is "the text of a communication to the 8t. Louis Glohe- 

 Democrat, written under the date of St. Joseph, August 21, 

 in which the writer tells how the good people of this city 

 have gone daft on asti'onomy, and how abstruse scientific 

 problems are taking the place of practical questions of the 

 day " : — 



In accordance with your positive instructions to proceed 

 by first train to this city, "for the purpose of making a 

 thorough investigation into the effect which the residence of 

 Professor llichard A. Proctor in St. Joseph has had thus far 

 upon the mental condition of its inhabitants," and to " lay 

 the result of the inquiry before the readers of the Glohe- 

 Democri(t without unnecessary delay," I have the honour to 

 report as follows : 



It was only when I reached Richmond and Lexington 

 Junction, several hours distant from St. Joe, that I began 

 to feel how powerful and widespread had Professor Proctoi's 

 influence become, While the train was resting at the 

 junction 1 overhead the baggage- master .saying to the 

 conductor : 



" There will be a meeting of the Pateetown Philosophical 

 and Astronomical Society this evening. We are going to 

 discuss the physical features of Jupitei'. Can't you drop in 

 and see us f " 



" I am very sorry," replied the conductor, " but a brief 

 lecture which I have promised to deliver before the Perigee 

 Club of North St. Jo.seph will preclude the possibility of my 

 attendance." 



" On what subject will you address the club?" asked the 

 baggage-mastei'. 



" Oh, I simply desire to lay before it a few thoughts which 

 I have prepared on the perturbations of Uranus," replied the 

 conductor. 



It was then that I began to realise the importance of my 

 commission, for I felt that I must be shortly landed in the 

 very vortex of philosophical and astronomical disputation. 

 If the railroad men, seventy-three miles away from the Pro- 

 fessor's new American home, were tilled with a burning 

 desire to explore the mysteries of stellar space, what, thought 



