A CURIOUS CALCULATION.

New Zealand Times, Volume XXX, Issue 4346, 23 February 1875, Page 3

A CURIOUS CALCULATION.

(From the Melbourne Leader.) Mr. E. A. Proctor has published some curious speculations on strange hands of cards, especially at whist. The calculation has been made, by Babbage, I believe, that if the entire population of the earth, taken at 1,000,000,000 persons, were to deal the cards incessantly day and night for 100,000,000 years at the rate of a deal by each person a minute, they would not exhaust the one hundred thousandth part of the number of essentially different ways in which the cards can be distributed. On the other hand, it is recorded that there are two well authenticated instances within ten years of one player holding all the_ in his own hand. Those who believe this say, “ Messrs, the mathematicians, see how a plain tale doth set you down !” Mr. Proctor takes up. the cause of the mathematicians, and shows that there is no improbability in the occurrence once, in ten years, of the whole of the trumps being -held by the dealer, because there is an immense number of ways in which this may be done. The thirteen cards may be dropped in any order, and the number of permutations in dealing the other. ..thirty-nine cards is enormous. Taking the first calculation for comparison, Mr. Proctor shows that the 1,000,000,000 inhabitants of the earth would have only to deal for one hour and fifty minutes for an even chance of ' giving all trumps'to one of the dealers, so that the remarkable hand would be held by some one or another at least thirteen times a day. Having ascer. tained this, Mr. Proctor sought ’to verify the usually received calculation, fimt abovementioned,' and found that it., fell far short of the truth, A cipher must have ‘been dropped somewhere, for only one millionth of the possible permutations would have been' gone through after all the inhabitants of the earth had been dealing night and day for a hundred million years. It is visually remarked that the human mind is incapable of grasping the vast figures recpiired in recording astronomical .facts, but Mr. Proctor has shown that even the distance of the fixed stars Measured in' hairbreadths is inconceivably smaller than the number of ways in which a pack of cards may be arranged; Taking the breadth of the finest spider’s web at the millionth part of an inch, he points out that the distance of the star Alpha Centaufi would contain this breadth, about 1,500,000,000,000,000,000,000,000 times. , But even this enormous sum would have to be multiplied by a number- containing fortyfour digits, that is by more than 10,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000 to amount to the number of ways in which the fifty-two cards might bo dealt in one lot, not in four as at whist. If this number were represented by counters 'consisting of cubes not bigger than the thickness of a spider’s thread along the edge, and these tiny counters were built up into a great cube, the size of it would be 7000 times the distance of the sun from the earth, that is, its length, its breadth, and its thickness, would each be of this enormous measure. The number representing the possible ways in which threads in a pack may be arranged is approximately 80,657,470,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000. It would be a problem of itself to give this number a name.