Answers 269- A COMMON DIVISOR
Since the numbers have a common factor plus the same remainder, if the
numbers are subtracted from one another in the manner shown below the
results must contain the common factor without the remainder.508,811- 480,608
28,203
723,217
- 508,811
214,406
Here the prime factors of 28,203 are 3, 7, 17, 79, and those of 214,406 are 2,
23, 59, 79. And the only factor common to both is 79. Therefore the required
divisor is 79, and the common remainder will be found to be 51. Simple,
is it not?- CURIOUS MULTIPLICATION
In the first column write in the successive remainders, which are 1 0000 1 1,
or reversed, 1 1 0000 1. This is 97 in the binary scale of notation, or 1 plus
25 plus 26. In the second column (after rejecting the numbers opposite to the
remainder 0) we add together 23 X I, 23 X 25 , 23 X 26 , equals 2,231. The
whole effect of the process is now obvious. It is merely an operation in the
binary scale.181. THE REJECTED GUN
The experts were right. The gun ought to have fired 60 shots in 59 minutes
if it really fired a shot a minute. The time counts from the first shot, so that
the second would be fired at the close of the first minute, the third at the close
of the second minute, and so on. In the same way, if you put up 60 posts in
a straight line, a yard apart, they will extend a length of 59 yards, not 60.
- TWENTY QUESTIONS
There are various ways of solving this puzzle, but the simplest is, I think,
the following. Suppose the six-figure number to be 843,712. (l) If you divide
it by 2, is there any remainder? No. (2) If you divide the quotient by 2, is