72 



KNOWLEDGE. 



[Maech 1, 1901. 



/. BaddeJey. — Prohably uot ; but if such a course should 

 be deemed advisable, a suitable warning vrill be given. 



E. Hunt. — Problems with more than one key mav 

 possibly be given intentionally in the later stages of the 

 competition. 



S. W. Billhtijs. — It is not necessary to give more than 

 two keys to any problem, or to say which is the author's 

 Intention. 



C. S. Hudson. — You will see that your suspicious are 

 correct. Considering the reputation of the composer it is 

 strange that these susj>icions were not shared by the 

 large number of other solvers who gave B to Q6 only. 



S. S. — Too late to reply to last month. You will sne 

 that yom- solutions were incorrect. 



W. F. P. — Solution of No. 1 correct, but Croydon post- 

 mark was February 11th. 



P. G. L. F. — Many thanks. They will appear next 

 month. 



a. J. Pearce. — Your communications have been handed 

 to me. That which is remotely connected with Chess is 

 noticed below. Please excuse my abstract of your jjaper. 



A table of the leading scores in the Solution Tourney 

 will be given next month. Meanwhile some apology is 

 due for the following attempts to atone for lack of difficulty 

 by means of additional- quantity. 



PEOBLEMS. 

 By C. D. Locock. 



No. 1. 



Black (8). 





^«^^^ ^''^'■'/ '/ ^^^' 





WMi W 





White (9). 



White mates in two moves. 

 No. 2. 



Black (7), 



»^_.,.,feSI^ » A 



wm^^,^,^/i,„^„,, 



BBS! 11:1 



Wbiti (15). 



"S^Tiitfi mates in two moves. 



No. 3. 



BlACK (10). 



White (10) 



White mates in two moves. 



CHESS INTELLIGENCE. 



An Old Chess-Board Puzzle. 

 Probably most chess-players are acquainted with the 

 device by means of which a chess diagram may be cut 

 into four pieces and fitted together in such a manner as 

 to form a rectangle of apparently 65 scjuares. The 

 method is as follows : Cut oft' the 24 top squares of a 

 diagram, and cut that piece into two halves diagonally, 

 from corner to corner. Then cut the larger piece of 40 

 squares along a line drawn from the left hand bottom 

 corner of Qscp to the right-hand toji corner of K5. By 

 fitting these pieces together, a rectangle, apparently lo x ."i, 

 mav be obtained. 



Mr. R. J. Pearce, of Auckland, New Zealand, sends a 

 mathematical exposure of the fallacy. I have not space for 

 his piroof, and am doubtful whether it would lie intelligible 

 to all the readers of this column; but the gist of the matter 

 lies in the fact that while the " fitting " along the lines CD and 

 EFis quite correct, the "fitting" along AB is by no means so 

 accurate. In fact AB, so far from being a straight line, 

 is in reality an attenuated rhomboid, ACBF, having an 

 area exactly e([ual to that of one square of the chessboard. 

 That is, the complete figure is composed of diagram paper 

 amounting in all to <i4 squares intersected by a small 

 rivulet of ink or other paper equal in area to one square ; 

 the result l.ieiug a true rectangle of an area equal to 65 

 squares. The difficult part of Mr. Pearce's proof lies of 

 course in calculating the area of the -parallelogram ACBF. 



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