THE CATTLE PROBLEM OF ARCHIMEDES. 665 



right-end which were computed by the Hillsboro Mathematical Club. 



This solution is published in the American, Mathematical Magazine 

 for May, 1895, where Bell remarks that each of these enormous numbers 

 is ' one half mile long.' A clearer idea of its length may be obtained 

 from considering the space it would take to print it. Each page of 

 this Monthly contains 45 lines and in each line about 50 figures may 

 be set, so that one page would permit a number of about 2,250 figures 

 to be printed. To print a number containing 206,545 figures there 

 would be required 92 pages,- and to print the nine numbers indicated 

 above a volume of about 830 large octavo pages in this size of page and 

 type would be needed. 



It is known that Archimedes speculated regarding large numbers, 

 for his book called Arenarius is devoted to showing that a number may 

 be written that will express the number of grains of sand in a sphere 

 of the size of the earth. It can not be proved that Archimedes was, 

 or was not, the author of the cattle problem, but, as Amthor remarks, 

 the enormous numbers required in its solution render it worthy of his 

 genius and proper to bear his name. Its closing challenge still remains 

 open, for the complete solution has not yet been made. Moreover, it 

 is practically impossible that the long numbers can ever be computed, 

 since the investigations of Bell show that this would require the work 

 of a thousand men for thousand } r ears. The little prairie town of 

 Hillsboro may, however, well exult as a conqueror, for its mathematical 

 club has made the most complete of all solutions of the cattle problem 

 and has proved itself to be highly skilled in numbers. 



