"Let me hear what you know about it." Hamilton closed the book. "I think I have it fairly straight," he said. "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. The actual address, street, and house number, and everything else we get by reference to the schedule." "That's enough!" cried Hamilton. "I can see now. It would take a sheet of paper a city block long merely to write down the figures." "If you wrote down end to end all the possible relations that forty-eight figures could be put into you'd need a lifetime to write them down. Why, just with an alphabet of twenty-four letters, Leibnitz the great mathematician, calculated that over six hundred septillions of easily pronounceable words, none over three syllables long, could be arranged. We have room enough to arrange any trifling little matter like seventy or eighty million addresses, although, in truth, the gang-punch merely provides the district and section of district, and the schedule would give the rest if we had any need to refer to it." "I see," said Hamilton, "and I suppose a number is put on the card which corresponds with every district number on the schedule. Then I come in on all the rest of the card." "Yes, every other hole is punched by the clerk." "But this machine doesn't seem to punch," the boy objected; "I put in a canceled card just now and tried it, but when I put the key down, nothing happened, the key just stayed down."