The sun. [volume] (New York [N.Y.]) 1833-1916, 1909-05-16
THAT TROLLEY CAR TBIcK.

A large number OF solutions, some oil
them worked out with great care, were
sent in to decide how much money was &c
change hands on that little bet between
dials in a trolley oar. The trap in the prob
lem, II it may be called a trap. lies u the
fact that. az stated in the original, printed
three weeks ago. the lower space for the
numbers = has five figures and Is capa-
BILE 81 going as high as ee.gee. A large
number OF solutions, while correctly
calculated. forgot to allow for the con,
these five figures began with zeros.
Those who are not familiar with the
working OF problems OF this kind should
be informed that the chances that two
figures will not be alike Is found by multi.
plying the number OF figures possible 10
the first space by the number that vii,
space. Thus, there may DO any one Of
ten figures In the first, and any q Of nine
different from the n selected for the
first, for the second place. The selection
for these two having been made, there
are only eight figures available for the
third space, only seven for the next and
figures would produce duplicates.
II all the numbers were calculated for.
regardless OF duplicates. all ten would be
available. and we should multiply i0xl0x
ioX i0x 10 to get 100. OOo variations posi-
BILE on the dial. which 10 simply beginning
with 1 and going one beyond %, 900 to
oo, 1000. OF these ioo. 900. the numbers that
multiplying l0xsxsx7Se=So.e+ 40. This
number represents Browns chances OF
winning on the lower dial. as against the
90, TOO for Adams. because Brown wins
only when the figures are not alike.
But while Adams loses 5000 times on
the lower set he wins once in ten tim 70
in the upper set, which is s.o24 to be added
against Browns 27.3ie. Reducing this to
dollars Adams comes out S<5-Ss.s ahead.
Several ask how Brown came TO make
such q foolish bet. Fol the same reason
that 30 many persons who arc ignorant
Of the laws OF probabilities bet on chances
that they do not understand:
Brown knew that on the dial with only
two figures In IL he would win nine times
out Of ten, and he imagined that he would
have the same chance or the dial with
Eve figures in II. What he gained on the
upper dial was completely wiped out by
his losses on the lower.
Correct solutions from; Algernon
W. w. Dudley. Oscar Soheurmann. N.
Mann, j. W. Cromwell, Jr.; Newman d.
Waffle, W. r., T. W., and Z. d. Harper.
CURIOUS FIGURE ARRANGEMENTS.
Here are II couple Of puzzles OF quite
q different kind. which will probably
afford some amusement before the solu-
ton Is found. They are what might be
called in lighter vein,' be ing more suited
TO the younger members OF the family
than to the alRebraiosl cracks who have
been wrestling with trolley cars and
farmers ten acre lots.
Take the ten figures i2st567se0--
and see II you ~ arrange them In such
a manner that they will add up exactly
a hundred, using some Of them az vulgar
fractions II you like. and placing between
them Of the mathematical signs.
Here Ia another one after you have
solved that, and one which will need a
little thinking as well AS figuring: Put
down sixty and subtract nine from II
take what remains from seventy and still
hays the remainder even.