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Problem 619: Miodrag Mladenovic - Helpmate

miodrag(31.10.2015) Miodrag's original helpmate shows the recently popular and complex idea "Perpetuum Mobile" in which twins are the first black move of the previous two solutions!

619. Miodrag Mladenovic (Serbia)
  H#2*      2 sol.      (10+9)
a) Diagram
b) After first move of (a)
c) After first move of (b)
d) After first move of (c)
 a) 1...Bf4+ 2.Kd4 e3# 
1.Se6 Bf2 2.Sd4 Bg3#, 1.Sd3 Sc4+ 2.Ke4 exd3#
b) (after 1.Se6) 1...Bf2 2.Sd4 Bg3#
1.Sc5 Bf4+ 2.Kd4 e3# 1.Sf4 Bc5 2.Sd5 Sd3#
(after 1.Sd3) 1...Sc4+ 2.Ke4 exd3#
1.Sc5 Bf4+ 2.Kd4 e3#, 1.Sf4 Bc5 2.Sd5 Sd3#
c) (after 1.Sc5) same as in a)
(after 1.Sf4) 1...Bc5 2.Sd5 Sd3#
1.Sd3 Sc4+ 2.Ke4 exd3#, 1.Se6 Bf2 2.Sd4 Bg3#
d) (after 1.Sd3) Same as in b) second solution
(after 1.Se6) Same as in b) first solution
Perpetuum Mobile, Model mates, Merry-go-round (Author)


+3 #1 Miodrag Mladenovic 2015-10-31 07:00
Just to clarify my problem a little bit. I think that this is the first problem showing this teme with two solutions. Basically this problem has four different initial positions with bSc5 -> e6 -> f4 -> d3. The problem could be published as four twins with stipulation H#1.5. There are four model mates and all black and white moves are different.

However it's paradox to have perpetuum mobile where bS is doing a real "merry-go-round" in both directions.

It's also possible to show perpetuum mobile theme with two solutions and set play in some trivial positions with three solutions. For example: 3R4.8.1r6.3B4.KP1kPP2.6P1.3S4.8
(I am not sure how to place diagram here). Although this is the correct problem in my opinion it does not deserve publishing. I placed it here more to present this idea with three solutions.
+2 #2 Seetharaman Kalyan 2015-10-31 07:50
Diagram for Miodrag's simpler example:

H#2 2 Sol.
1.Rf6 f5 2.Ke5 Sf3 #
1.Rd6 e5 2.K*d5 R*d6 #
1.Rd6-b6 b4-b5 2.Kd4-c5 Sd2-b3 #
1.Rd6-f6 f4-f5 2.Kd4-e5 Sd2-f3 #
1.Rf6-b6 b4-b5 2.Kd4-c5 Sd2-b3 #
1.Rf6-d6 e4-e5 2.Kd4*d5 Rd8*d6 #
+2 #3 Seetharaman Kalyan 2015-10-31 08:00
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