Dec. 30, 1881.] 



♦ KNO^VLEDGE • 



1S5 



t is very hard that space shonld bo taken op with qncBtions, the 

 answers to which are in well-known text-books. May I suggest 

 that such questions be not inserted, but answered shortly in the 

 pmall print " Answers to Correspondents." 



1 also thought it very hard that so much room was given for 



■ that the sun is cold," to men whom you say cannot comprehend an 

 argument derived from the solar dark lines. — Yours, &c., 



Anti-Pakadox. 

 [Anti-Paradox's letter is allowed to appear as a rather remarkable 

 ■pecimen of the class to which it belongs. A m ong some twenty or 

 ihirty kindly letter, recognising what -we are trying to do in 

 Knowledge, and, indeed, giving us credit for a degree of success 

 Idch we ourselves would hardly claim, will come a letter or two 

 :ih as the above. Anti-Paradox's complaint reminds us of a 

 mark of a theatrical agent we met in New York, -who said there 

 ,ire some who would not go to the theatre " uidess they had 

 : i!ers given for all their family, and then they complained unless 

 r.-t-class carn'agcs were sent to take them along." Putting 

 .usido the question whether those who have queries to ask 

 have not a right to expect some space, and nating that many 

 (irimers and text-books are not simply worded, even when 

 (which is not always the case) they are exactly described, we 

 would invite " Anti-Paradox," and the small proportion of our 

 readers who view matters like him, to consider things from the 

 (loint of view of the proprietors of such a journal as this. " Anti- 

 Paradox " pays twopence for each copy, of which sum more nearly 

 the half than three-fourths reaches the proprietors of Knowledge. 

 Let " Paradox " inquire how much twelve, fom'teen, or sixteen double 

 I paves (as the case may be) of good paper is likely ts cost, even at 

 V, liolesale rate, and the probable expense per copy of such matters 

 ~ composing, printing, folding, advertising, and so forth, to say 

 ■thing of editing. When he has done this, and notes the nature 

 uf the margin between a penny-farthing and such costs per copy, 

 let him ask himself if it is quite reasonable for him to expect us to 

 crowd queries, correspondence, &c., into "the small print ' Answers 

 to Correspondents,' in order that lie may have as nearly as possible 

 the entire contents of Knowledge devoted to original matter. 

 Obser\-ing that a page of small print in itself involves a loss (cost- 

 ing more than twice as much as a page of largo print), let him 

 notice that, on the average, we give him, as it is, as much original 

 matter as would make the sixth part of such a work as my 

 "Light Science" or Professor Wilson's "Leistire Hour Studies" 

 — so that, for a shilling, he gets as much of such matter 

 (fresh and fresh) as in such volumes costs six or seven 

 shillings. It is " a very hard thing," he considers, " that we 

 do not fill our entire space \vith matter so costly that if we 

 did, the greater the sale, the greater would be the proprietors' 

 lo-s. It would be, we venture to tell him, a "very hard thing" 



■ our reward for givivg six or seven pages of extra space to corre- 

 ■indencc should be a claim for so much more original matter. It 



" a very hard thing " to find room for so much original matter 



- we insert, and also to give space for correspondence, queries, &c., 



ithout making the proprietors cry out lustily at our extravagance 



' onsidering the price of Knowledge). If we had many snch 



'ii erful correspondents as "Anti-Paradox," this " very hard thing " 



■ >i;ld simply become impossible. We beg, on the proprietors 

 'half, to remind " An ti- Paradox" that the " verj' hard thing" 



which affects him is an infliction of his own choosing. He is not 

 obliged to bring this terrible hardship on himself by expending the 

 Buni of twopence weekly on Knowledge, and then groaning because 

 we answer queries in other than our smallest type, or admit in- 

 quiries from readers who do not fnlly appreciate the significance of 

 The solar dark lines. To our more just and generous readers we 

 ay that we do the best we can to oblige all ; we gi'.o to each class, 

 rrcspondcnts, querists, mathematical students, chess and whist 

 I aycrs, and original writens, more space than we can fairly afford. 

 We feel satisfied that so long as wo do so, the proportion dis]>osed 

 to be as unreasonable as "Anti-Paradox " and a few others have 

 hown themselve.o, will be very small indeed. — The Editob.] 



THE FIFTEEN PUZZLE. 



[154]. — The following is a solution to the Fifteen Purzle, starting 

 from the lest position : — 



Let R = right L = leftU = np .and D — down. 



12. D.— 11.10.9. K.— 13. U.— 15.14.12. L.— 11. D.— 10.9.13. E.— 

 15. D.— 14.L.— 13.D.— 9, &c., to L until the figures of the last two 

 rows read. 



10 11 



12 



Then move: 15.14.13. R.— 9.5.1. D.— 2.3.4. L.— 8.12.13. U.— 

 14.15.9. K.— 5.1.2. D.— 3.4.8. L.— 12.13.14. U.— 15.9.5. R.— 1.2.3 D. 

 —4.8.12 L. 



Then turn the box so that 



Then move: 14.13. R.— 11.10. D.— 6. L.— 7.U.— 14. U.— 15.11 R. 

 —9. D.— 10.14. L.— 11. U.— 15. R.— 14. D.— 11.12. L.— 13. U.— 

 15.14.9. R.— 10. D.— 11.12.13. L.— 15. U.— 14. R.—13.D.— 12.11. R. 

 —10. U.— 9.13.14. L.— 15. D.— 12.11.10. R.— 9. up.— 13.14.15. L. 



Wishing success to your valuable paper, — 1 remain, yours trtUy, 



Yawnups. 



[The position attained by '■ Yawnups," which, of course, he does 

 not regard as an actual solution of the problem, for which a money 

 prize was offered in America, can be more readily reached ; in fact, 

 we do not see the plan of " Yawnups' " solution, many of the moves 

 in which seem to be wasted. The actual number of moves in his 

 solution, counting such a move as 9.13.14. L as three moves, is 102. 

 By the following method the position is attained in 57 moves. It 

 may, perhaps, be done in fewer, but the solution is straightforward, 

 and its stages illustrate the method of dealing with snch difficulties 

 as occur in all " fifteen " problems :— 4.8.12. D.— 12.3. R.— 13.9.5. U. 

 —15.14.12. L.— 3.4.8. D.— 5.1.2. E.— 15.13.9. U.— 14.12.8. L.— 

 2.3.4. D. — 1. E. Now turn the box so that right hand runs 



iH N CO -^ 



after 28 moves. We next get 5, 6, 7 right by the following 

 moves:— 7.11. L.— 10. U.— 6. L.— 11. D.— 7. R.— 5. U.— 6.11. L.— 

 10. D. — 7. K. — 6. V. The two upper rows are now right, after 

 12 moves more, or 40 moves in all thus far. The last two lines 

 now run thus : — 



01 r^ ,- ^ 



To get these right proceed thus : — 11. R.— 9. U.— 13.15. L.— 10. D. 

 11. R.— 15. U.— 10.14. L.— 12. D.— 11. L.— 15. E.— 10. D.— 14. L.-^ 

 15. D. — 11. L.12.— U. The last two rows are now right, after 17 



more moves, or 57 moves in all. The blocks are now in the order 

 which we may regard as one of the only possible forma of solution 

 from the " lost position." — Ed.] 



We have since received the following solution in 60 moves — 

 13.15.14. E.— 1.5.9. D— 2.3.4. L.— 8.12.14. U.~9.13.15. E.— 2.1.5 D. 

 —3.4.8. L.— 12.14.15. U.— 5.9.13. R.— 3.2.1. D.— 4.8.12. R. One Une 

 is now right in 33 moves. Then : 14.15. U.— 10.11 E.— 6. D.— 7. L. 

 Two lines are now right in 39 moves. 15. E. — 11. U. — 13. U. — 9. E. 

 —10. D.— 15. D.— ll.L.— 14. D.— 12. E.— 11. U.— 15. U.— 13. L.— 

 14. D.— 15. R.— 11. D.— 12. L.— 15.14. U.— 13. B.— 10. U.— 9. L.— or 

 all the numbers right in 60 moves. 0. F. W. 



