Evening star. [volume] (Washington, D.C.) 1854-1972, 1880-03-06
THE eAH or FIFTEEN.


| Various Solutions.
II Is possible that the publication OF solution
| OF the famous puzzle may interrupt rudely the
reyertes OF The philosophers who have either
leisure to ton over its intricaciea But the con-
vlcuon that the solution will bear an olive
| pIanch OF Eeace to countless stricken house
spirit OF broad philanthropy, TO offer what
appears TO oe one Of the several keys to the
4. game.
us first agree that the row Of numbers next to
the side OF the box from the holder, and contain
Ing the numbers l, ., and shall be called A.
5. and S, be called B; and the third row, con-
We shan see thas and G are the Ii important
AT. the outset, instead of getting the lower
numbers In their numerical order, the quicker
way to solution Is to arrange eleven numbers
In their proper order on the outside rows Of the
box. That order, it Will be seen, is 1, 9, g. As
IL. Is, u, 13 g. s, and we can begin with any one
Of these numbers and work either one way or
both ways. This order can be quickly secured
by using the four central squares and three
blocks Move into the central square the outer
block, {any one of those numbered above,) turn
IL until oIpostte its proper place and make a
vacancy for it by removing a block from an
other part Of the outer rows and shifting the
outer blocks around. SO easily is this done that
We leave 1t 10 the ingenuity Of our readers with
out further instructions.
The outer blocks having been arranged, the
puLLiC 10 uulltSu " lOuI CtuITdl SQudT6S
and the numbers 6, I, 10 and II, which viii
rarely come In their proper order. These four
numbers are susceptible. Of twenty -four COM
hereafter. may be resolved into two, namely,
double inversion I'm row I, and row c II. 10
and single inversion, row correct and IL, 10
follows, understanding the mandatory word
move before each OF the numbers which follows:
p. 70, H. I, 10, s. II, G, 10, 76, 10, 49,
Let the foregoing formula be called X.
The single inversion trow B correct and II, 10
in row 9, which seems to involve the whole
the. following numbers in the order pre-
scribed:
12,s, I, 1o,n 1o.7, s, II, !, 10, 6, III, 9,
CT. IL, 8, IL. We now have I, II In row B and
| 6, 10 in row c: Move all the outer blocks until
number is shifted four places and is next to 8.
Move the box one-quarter around, and 1t will be
seen that the solution Is complete Let the fore
going formula be called Y.
We have disposed Of three Of the twenty four
combinations possible with the four central
numbers. The three are: ~ the right order, (9
one double inversion, and (3) one single inver-
sion. Any one of the remaining twenty-one
combinations can be quickly converted into one
OF the foregoing three by applying to them re-
peatedly the methods Of moves in formula, or
the method represented in the first eight moves
in formula \, or both methods combined. The
moves are to be the same, though the order OF
numbers will, Of course, be different. For
mula x; and also its first eight moves
fore any conversion Of the twenty-one COM
btnations is tried. After the double or single
inversion is obtained. they can then be solved
by formulas and Y, respectively. AN this
which appears complex and difficult on paper.
will be readily understood when the box can be
used for Illustration. The time for solving the
puzzle from the beginning is from four to ten
minutes
ANY possible combination Of the numbers can,
in the way we have explained, be merged into
trail blocks, and then solved by the formulas
given: This applies, OF course to the final
OF 10 ID l and 49, H. and ~
and tempers OF our provincial friends In Roch-
ester.
correspondent of the Philadelphia Bulletin
supplies the following solutions: The new
"Gem Puzzle" or "Game of Fifteen" has sprung
suddenly into such wide popularity, and ques-
lions as to the poss1ollity Of solving the pro,
order being often raised, word or two may not
be inopportune at this moment
First. The object being 70 arrange the num-
bers in consecutive series, the position OF the
numbers on the blocks would seem to be of no
importance, so that whether the figures are in
their natural position or whether they lie on
their side with reference to each block Is un-
Second. While it is possible to reach the de-
sired solution by chance, the only certainty of
doing 50 is by proceeding according to def
Third. 1t is possible to solve the problem by
commencing the series at any corner, or allow
ing 1t to end at any corner, and by making the
direction of increase of the numbers from right
to left or from left to right, or from top to bot
tom or from bottom to TOP It t. follows from
The beginning or the end or at any desired
square.
The final arrangement depends upon two
hfngS, VIZ: First, whether one begins to ar
range the numbers from the lowest upward, or
from the highest downward Il. e., /, Q, 8, &C, or
r. 49, &C, secona whether the course Of
H1th the hands OF watch or In the opposite
direction.
the cover Il he Cox containing the puzzle. e.,
The No. In the left-hand upper corner and a
flank space in the lower right-hand corner, one
ane spS snd the
box. increasing in the direction of the motion OF
The hands Of watch up to No. II. There will
then be one blank space left in the outer rows.
which Will permit the whole series to be moved
forward or backward until the one is in its
proper place. The four numbers in the middle
must hen the order 12 rs
numbers can be shifted until they either appear
in this order OF as follows: 1412 above 1915. In
the first case the outside series is moved up till
the is at the upper left-hand square, and the
at the upper r1ght-hand square. The first row
being in order, the 5 and the three following
figures move of to the left on the second line;
pushing 1915 before them until the second row
is in order The numbers will then be In such
position that by pushing the 9 to the left square
Of the third row the series will be complete.
The same effect in reverse order can be OBJ
tanned by carrying the train Of figures with the
at the head in the opposite direction. or with
the hands Of watch, and having the NUMBERS
in the middle thus: 1912 above 1914. In this
case the series will commence at the rtght-hand
upper corner and read to the left, and the blank
space will be at the lower left-hand corner.
Precisely the same tactics as those first de-
scribed, with the two differences of making Is
the head of the column instead OF l, and bring
ing it to the nght-hsnd lower squares, when the
numbers in the middle are as follows: IL above
a. will result in the natural series but the blank