## THE MILLIONAIRE'S PERPLEXITY.

(

Money Puzzles)

Mr. Morgan G. Bloomgarten, the millionaire, known in the States as the

Clam King, had, for his sins, more money than he knew what to do with.

It bored him. So he determined to persecute some of his poor but happy

friends with it. They had never done him any harm, but he resolved to

inoculate them with the "source of all evil." He therefore proposed to

distribute a million dollars among them and watch them go rapidly to the

bad. But he was a man of strange fancies and superstitions, and it was

an inviolable rule with him never to make a gift that was not either one

dollar or some power of seven--such as 7, 49, 343, 2,401, which numbers

of dollars are produced by simply multiplying sevens together. Another

rule of his was that he would never give more than six persons exactly

the same sum. Now, how was he to distribute the 1,000,000 dollars? You

may distribute the money among as many people as you like, under the

conditions given.

## Answer:

The answer to this quite easy puzzle may, of course, be readily obtained

by trial, deducting the largest power of 7 that is contained in one

million dollars, then the next largest power from the remainder, and so

on. But the little problem is intended to illustrate a simple direct

method. The answer is given at once by converting 1,000,000 to the

septenary scale, and it is on this subject of scales of notation that I

propose to write a few words for the benefit of those who have never

sufficiently considered the matter.

Our manner of figuring is a sort of perfected arithmetical shorthand, a

system devised to enable us to manipulate numbers as rapidly and

correctly as possible by means of symbols. If we write the number 2,341

to represent two thousand three hundred and forty-one dollars, we wish

to imply 1 dollar, added to four times 10 dollars, added to three times

100 dollars, added to two times 1,000 dollars. From the number in the

units place on the right, every figure to the left is understood to

represent a multiple of the particular power of 10 that its position

indicates, while a cipher (0) must be inserted where necessary in order

to prevent confusion, for if instead of 207 we wrote 27 it would be

obviously misleading. We thus only require ten figures, because directly

a number exceeds 9 we put a second figure to the left, directly it

exceeds 99 we put a third figure to the left, and so on. It will be seen

that this is a purely arbitrary method. It is working in the denary (or

ten) scale of notation, a system undoubtedly derived from the fact that

our forefathers who devised it had ten fingers upon which they were

accustomed to count, like our children of to-day. It is unnecessary for

us ordinarily to state that we are using the denary scale, because this

is always understood in the common affairs of life.

But if a man said that he had 6,553 dollars in the septenary (or seven)

scale of notation, you will find that this is precisely the same amount

as 2,341 in our ordinary denary scale. Instead of using powers of ten,

he uses powers of 7, so that he never needs any figure higher than 6,

and 6,553 really stands for 3, added to five times 7, added to five

times 49, added to six times 343 (in the ordinary notation), or 2,341.

To reverse the operation, and convert 2,341 from the denary to the

septenary scale, we divide it by 7, and get 334 and remainder 3; divide

334 by 7, and get 47 and remainder 5; and so keep on dividing by 7 as

long as there is anything to divide. The remainders, read backwards, 6,

5, 5, 3, give us the answer, 6,553.

Now, as I have said, our puzzle may be solved at once by merely

converting 1,000,000 dollars to the septenary scale. Keep on dividing

this number by 7 until there is nothing more left to divide, and the

remainders will be found to be 11333311 which is 1,000,000 expressed in

the septenary scale. Therefore, 1 gift of 1 dollar, 1 gift of 7 dollars,

3 gifts of 49 dollars, 3 gifts of 343 dollars, 3 gifts of 2,401 dollars,

3 gifts of 16,807 dollars, 1 gift of 117,649 dollars, and one

substantial gift of 823,543 dollars, satisfactorily solves our problem.

And it is the only possible solution. It is thus seen that no "trials"

are necessary; by converting to the septenary scale of notation we go

direct to the answer.