Grant County herald. [volume] (Lancaster, Wis.) 1850-1968, 1880-04-01

without lifting a number from the box or
without sliding one number past another, I'M
I'll you have them arranged consecutively as
they are in Fig B. To DO this is the puzzle
II will be found not difficult to arrange the
three full rows, but if the other three mum,
bers- the Is, IA, lido not a. the same
time come out in their proper order, the diff
fcult part of The solution is still ahead, and
now that oil America has racked its brains
over the different combinations, it is admitted
that If these numbers, after the others are
arranged, are found to stand Is, IA, Is or IA,
Is, 10 or Is. Is, IA, their consecutive ar.
rangsment is not possible. Hence It is a
proper puzzle only when after the full rows
are arranged these are found to be consecu>
tive or stand IA, IS, Is, or Is, Is, IA. That
is. in setting your figures in the box, there are
three chances in which solution il possible
and three wherein II is not possible. and un.
less your head is longer than Paul Morphy's
you osn's toll whether you have soluble
puzzle before you until you get the numbers
arranged down to the last three.
Puzzles are sometimes good mental exer-
cises. This has given rise to review of
very able one, which is to arrange the first
sixteen cardinal numbers in such a square as
that all the rows up and down and right and
left and diagonally, shall foot up 81 Az
study We will take the numbers consecutively-
thus:
IIT2TsI4I The tyro at first thought
6IeI7s would think this simplest of all
IoIloIlil2i arrangements the farthest posi-
Ilsll.Ilollol BILE from the desired solution, but
an examination will show him it is nearly
done already. Add the two rows from corner;
to corner; the sum Of each is "a. Add any two
opposite rows, as the right and left or
top and bottom or the two middle rows
across or up and down, and the sum of any
two thus selected is just twice 81. Take any
two opposite pairs, as and . in the upper
left hand corner and Is and 10 in the lower
right hand corner and their sum is 81. Try
also and 4, and Is and IA; and 5, and 10
and Is. and 8, and and Is; 2 and 8, and
IA and Is, sc. The sum of the four corner
numbers is "a; aud the sum of the four mid
die numbeIsis 81. These facts suggest an easy
and systematic exchange of numbers, to have
all the rows up and down and right and left
foot 81. Let the l6 and ! change places
also the IS and 4; the and 8, and the IA
and Is; the and 8, and the 8 aud IL. Now
your diagram appears thus:
1851 sT2II3 The rows, any way you take
el6 I Il them count 81. The four middle
IlonI numbers count 81. So do the
llsll4l four corner numbers Divide the
square into four squares of four numbers each
and the numbers in the small squares will
each count 81 Take any two oppo site
pairs relatively situated and their sum is "a.
We have counted S8 orderly groups in this
square wherein four numbers will mske the
sum of "a. And this is not the only arrange
msnt these numbers can have as solution to
the puzzle. The numbers /, 4, Is, l6 do not
need TO be in the corners and 8, 7, 10, IL do
not need to be the middle figures But the
other arrangement, we leave for those who
delight in making their own discoveries. As
between the l3, Is, Ia puzzle and the 81
puzz lie we decide the "a puzzle much the
more sensible of the two.