The sun., 1910-01-30

| The question was not what would happen
II these practical everyday appliances
were purely imaginary. friction, weight
and equilibrium being eliminated, but
what would happen II the monkey climbed
a real rope rove through a real pulley
in real life.
From this point OF view il was held
by those solvers who said that it de-
pended upon whether the monkev climbed
steadily or with a series OF .-sr-S
II problems based on theory are wanted,
how is this one?
Suppose that man il sitting in a boat
and that he wishes TO push from him
another boat in which there is asleep a
man that he has just robbed. To please
the theorists, suppose that the boats
are both ahoat on an ocean which 10 abb
solutely free from friction and that IL
has no shores. Call the spot where the
robbery takes place Long o.. and suppose
that the propelling force OF the push0H
In in a direction due east and west. Which
boat will be the fsrthest from Long o.
when they come to rest. the pusher or
the pushed?
SOME MORE ALGEBRA.
A number OF attempts have been made
to solve the problem printed two weeks
ago: t(4-txla=e1.e .ewhere D and
are rational fractions. Here is one from
Expand and we have
27-27p+sv-v+84+4s 4sr 17x' trs=o1.
Collecting and transposing, c'+i2rst
Il Is o6SIou. that and y must have the
celed won 70 si In the addition; also that
Is numerically greater than Z. there
fore 1t remains only to find a ratio be-
tween the nunerators Of and v.
Let v=2t. then substituting. collecting
hnAa NJ - q nAt rational Lat
and the result is 2ex'-eSr- tss-0. again
irrational. But " we let t==tr the edua-
tion becomes osx'-i5er Fec. where r==3
or - -
II r=:. then U.s. but this makes the
one term so negative. 50 we must
discard it. MI II III y
"a +r+ ~
(D'+(s)'=
l7ls7 ssoes4 s377siu
s7eI s2si p2ei
As large number Of readers seem to
be Interested In this clsss Of puzzle. here
Find the value Of the infinite ssries;
44+s.ssa - . .
The solution OF chess problem No. 50
is R--QR So, KxR. K-B2. forcing black
to advance the KIP. The point which
the majority Of solvers missed In this
which they give as K-Bsq. instead of
b. After all the pawn moves have been
made the error win be apparent, as the
king. II on the eighth row would DO IN
check.
J. j. Cox. William II. Baker, T. @. B..
Arthur B. Ettineer, N. d. W.. Charles
willing. j. H. MacGrorty. II: X; Thaw.
Edith Z. Behrens. 9. D: T.. F Powers;
Gregory.
7 Every now and then some enthusiastic
chess player sends In his analysis OF a
problem which he does not think was cor
rectly solved. As a rule all these COM
ments are unsound. but occasionally ons
Here is one from DR.. A. n. Baldwin OF
Norwalk, which points out q very ir-
genious defence for black In the position
shown in No. 7, printed IN THE suN on
February 20 last.
This was the position:
Waite. Black,
Q on KKts K on KR7
K on KKtl B on KKt7
Pom KB7
r on KS
In Bachmann's 'SchAchpArtien.' ",
pare l22. the solution is given as printed
in TIE Sun and IL has stood the eKamina-
ton OF chess masters for years. The
idea OF it was 70 check at RS and then
move the Q to o., pinning the pawn.
If the r tries TO win the Q by a check.
K-Kts draws by stalemate. II the
X moves TO Bs. Q-Qs ch starts per-
petual check.
Instead Of this DR., Baldwin suggests
that after Q--Q4 black should play
R--K2, forcing the @ to stay on the dag
onal or free the pawn. Then this follows;
White. Black.
K-Kts R-KB7
OBS or Kts R-B6 oh
K-Kt4 KRIS
: This 10 very clever, and it is certainly
remarkable that It has not been dis
covered earlier, which only goes to show
the infinite possibilities OF chess analysis.
Here is a position which contains an
lesson for the beginner:
CREss PROBLEM NO. 81.