"These first four columns
on the card I have nothing to do with, so far as I can make out; is that
right?"
"Yes," the older man replied, "that is looked after in another way. The
district and State and all that sort of thing go in that section, and
that is arranged by what we call a gang-punch."
"I don't know how that works," the boy said, "this list of instructions
to the punching clerk doesn't say anything about it."
"It doesn't need to," his informant answered, "for the simple reason
that the punching clerk has nothing to do with it. But I'll tell you if
you want to know. There are about seventy thousand enumeration districts
in the United States, and all we have to do is to set the gang-punch to
the number of the district."
"But there are not seventy thousand divisions on the card or anything
like it," the boy cried, "all told there are only forty-eight places in
those four columns."
"That works by the permutation of numbers," was the reply. "You can
arrange two numbers in only two ways, but you can arrange three figures
in six ways, four in twenty-four ways, five in one hundred and twenty
ways, six in seven hundred and twenty, seven in over five thousand ways;
ten would give you over three and a half million ways of changing them
around--and you can see for yourself where forty-eight would land you.
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