260 MISCELLANEOUS PROBLEMS [CH. XII 



part dissections of pairs of triangles, of a triangle and a 

 parallelogram, of pairs of quadrilaterals, of pairs of pentagons 

 each with two sides equal and parallel, and of pairs of certain 

 related hexagons. His results are projective and all of them are 

 deducible from his hexagon dissections. This is an interesting 

 generalisation. 



The solutions of these problems are lengthy, and almost 

 necessarily involve several diagrams. I content myself with the 

 above notes and references. 



The Window Reader. Some years ago a set of eight 

 numbered and perforated cards was brought out which enabled 

 an operator to state a number chosen by a spectator. Of the 

 eight cards each of the first seven was pierced with window- 

 like openings, each of the last seven contained some of the. 

 numbers less than 100 headed by the word Yes, each of the last 

 three had also certain digits on its back, and the first of, the 

 cards was headed with the word Top. Each card if turned 

 upside down bore on what was then its top the word No. 



The cards were employed to determine any number less 

 than 100 chosen by some one, say, A. They were used by B 

 thus. B first laid on the table the card numbered 1 with the 

 side marked Top uppermost. B then took the second card, and 

 asked A if the chosen number was on it; if A said yes, B placed 

 the card 2 on the top of the card 1 with the Yes uppermost; 

 and if A said no, B turned the card round and placed it with 

 the No uppermost. B then asked if the chosen number was on 

 the third card, and placed it on the top of 2 with the appropriate 

 end uppermost; and so on with the rest of the cards 4 to 8. 

 Finally on turning the whole pile over, the chosen number was 

 seen through the windows. 



The puzzle must have been widely circulated. It was sold 

 in Italy and in London, and friends tell me that they also saw 

 it in Germany. The method used is fairly obvious, and I will 

 leave to any reader, sufficiently interested, the task of con- 

 structing cards suitable for the purpose. 



Evidently, however, any number not exceeding 128 can be 

 determined by only seven cards, each bearing G4 selected 



