270 CALCULATING PRODIGIES [CH. XIII 



the 10th power: and he gave the answers so rapidly that the 

 gentleman who was taking them down was obliged to ask him 

 to repeat them more slowly ; but he worked less quickly when 

 asked to raise numbers of two digits like 37 or 59 to high 

 powers. He gave instantaneously the square roots and cube 

 roots (when they were integers) of high numbers, e.g., the square 

 root of 106,929 and the cube root of 268,336,125, such integral 

 roots can, however, be obtained easily by various methods. 

 More remarkable are his answers to questions on the factors of 

 numbers. Asked for the factors of 247,483 he replied 941 and 

 263 ; asked for the factors of 171,395 he gave 5, 7, 59, and 83 ; 

 asked for the factors of 36,083 he said there were none. He, 

 however, found it difficult to answer questions about the factors 

 of numbers higher than 1,000,000. His power of factorizing high 

 numbers was exceptional and depended largely on the method 

 of two-digit terminals described below. Like all these public 

 performers he had to face buffoons who tried to make fun of him, 

 but he was generally equal to them. Asked on one such occasion 

 how many black beans were required to make three white ones, 

 he is said to have at once replied " three, if you skin them" — 

 this, however, has much the appearance of a pre-arranged show. 

 It was clear to observers that the child operated by certain 

 rules, and during his calculations his lips moved as if he was 

 expressing the process in words. Of his honesty there seems 

 to have been no doubt. In a few cases he was able to explain 

 the method of operation. Asked for the square of 4,395 he 

 hesitated, but on the question being repeated he gave the 

 correct answer, namely 19,395,025. Questioned as to the cause 

 of his hesitation, he said he did not like to multiply four 

 figures by four figures, but said he, " I found out another way ; 

 I multiplied 293 by 293 and then multiplied this product twice 

 by the number 15." On another occasion when asked for the 

 product of 21,734 by 543 he immediately replied 11,801,562 ; 

 and on being questioned explained that he had arrived at this 

 by multiplying 65,202 by 181. These remarks suggest that 

 whenever convenient he factorized the numbers with which he 

 was dealing. 



