CH. IV] GEOMETRICAL RECREATIONS 73 



each husband travels with a harem of m wives or concubines ; 

 moreover, as Mohammedan women are brought up in seclusion, 

 it is reasonable to suppose that they would be unable to row a 

 boat by themselves without the aid of a man. But perhaps the 

 difficulties attendant on the travels of one wife may be deemed 

 sufficient for Christians, and I content myself with merely 

 mentioning the increased anxieties experienced by Moham- 

 medans in similar circumstances. 



Geodesies. Geometrical problems connected with finding 

 the shortest routes from one point to another on a curved 

 surface are often difficult, but geodesies on a flat surface or flat 

 surfaces are in general readily determinable. 



I append one instance*, though I should have hesitated to 

 do so, had not experience shown that some readers do not readily 

 see the solution. It is as follows. A room is 30 feet long, 

 12 feet wide, and 12 feet high. On the middle line of one of 

 the smaller side walls and one foot from the ceiling is a wasp. 

 On the middle line of the opposite wall and 11 feet from the 

 ceiling is a fly. The wasp catches the fly by crawling all the 

 way to it: the fly, paralysed by fear, remaining still. The 

 problem is to find the shortest route that the wasp can 

 follow. 



To obtain a solution we observe that we can cut a sheet of 

 paper so that, when folded properly, it will make a model to 

 scale of the room. This can be done in several ways. If, when 

 the paper is again spread out flat, we can join the points repre- 

 senting the wasp and the fly by a straight line lying wholly on 

 the paper we shall obtain a geodesic route between them. 

 Thus the problem is reduced to finding the way of cutting out 

 the paper which gives the shortest route of the kind. 



Here is the diagram corresponding to a solution of the 

 above question, where A represents the floor, B and D the 

 longer side-walls, C the ceiling, and W and F the positions on 

 the two smaller side-walls occupied initially by the wasp and fly. 



• This is due to Mr H. E. Dudeney. I heard a similar question propounded 

 at Cambridge in 1903, but I first saw it in print in the Daily Mail, London, 

 February 1, 1905. 



