286 CALCULATING PRODIGIES [CH. XIII 



the product of the digitals of its factors. Let us apply this in 

 Bidder's way to see if 71 is an exact divisor of 23,141. The 

 digital of 23,141 is 2. The digital of 71 is 8. Hence if 71 is 

 a factor the digital of the other factor must be 7, since 7 times 

 8 is the only multiple of 8 whose digital is 2. Now the only 

 number which multiplied by 71 will give 41 as terminal digits 

 is 71. And since the other factor must be one of three digits 

 and its digital must be 7, this factor (if any) must be 871. 

 But a cursory glance shows that 871 is too large. Hence 71 

 is not a factor of 23,141. Bidder found this process far more 

 rapid than testing the matter by dividing by 71. As another 

 example let us see if 73 is a factor of 23,141. The digital of 

 23,141 is 2 ; the digital of 73 is 1 ; hence the digital of the 

 other factor (if any) must be 2. But since the last two digits 

 of the number are 41, the last two digits of this factor (if any) 

 must be 17. And since this factor is a number of three digits 

 and its digital is 2, such a factor, if it exists, must be 317. 

 This on testing (by multiplying it by 73) is found to be a 

 factor. 



When he began to exhibit his powers in public, questions 

 concerning weights and measures were, of course, constantly 

 proposed to him. In solving these he knew by heart many 

 facts which frequently entered into such problems, such as the 

 number of seconds in a year, the number of ounces in a ton, 

 the number of square inches in an acre, the number of pence 

 in a hundred pounds, the elementary rules about the civil and 

 ecclesiastical calendars, and so on. A collection of such data is 

 part of the equipment of all calculating prodigies. 



In his exhibitions Bidder was often asked questions con- 

 cerning square roots and cube roots, and at a later period 

 higher roots. That he could at once give the answer excited 

 unqualified astonishment in an uncritical audience ; if, however, 

 the answer is integral, this is a mere sleight of art which 

 anyone can acquire. Without setting out the rules at length, 

 a few examples will illustrate his method. 



He was asked to find the square root of 337,561. It is 

 obvious that the root is a number of three digits. Since the 



