No.430,431 (PH)

No.430, 431 by Peter Harris – Two difficult for solving problems with elegant constructions! (JV)

Definitions:

Madrasi: Units, other than Kings, are paralysed when they attack each other. Paralysed units cannot move, capture or give check, their only power being that of causing paralysis. 

Transmuted Kings: When they are threatened, the Kings move only like the threatening unit(s).

PWC: When a capture is made, the captured unit (except a King) is replaced on the square the capturing unit just leaves. A Pawn is immovable on its 1st rank.

Maximummer: Black must play the geometrically longest move or may choose from among longest moves of equal length, distances being measured from the center of each square. Diagonal and oblique distances are measured from the orthogonal coordinates by using Pythagora’s theorem (take the square root of the sum of the squares of the orthogonal distances). All other orthodox chess rules apply.

No.430 Peter Harris South Africa original – 23.11.2013 Dedicated to Petko Petkov.   hs#4                                             (4+4) b) bSd5→g2; c) wBg1→b4 Madrasi Transmuted Kings     Solutions: (click to show/hide)   a) 1.Bg1-a7 Sd5-c3 2.Qa1-a5 Qg7-d4 3.Qa5-c7 Qd4xa7 4.Kh1-h2 Bb8xc7 # b) 1.Se2-c3 + Qg7-a7 2.Bg1xa7 Sg2-f4 3.Kh1-h2 Sf4-h3 4.Qa1-h1 + Ka8xa7 # c) 1.Bb4-a5 Bb8-e5 2.Ba5-c7 + Ka8-c6 3.Kh1-h2 Kc6-b5 4.Se2-d4 + Kb5xc7 # (С+ by Popeye 4.63) Convention is that a two solution problem is superior to a twin. There is an alternative view. In this problem there are parts (a), (b) and (c). In the diagram position, if the wBg1 was moved to b6 there would be 3 solutions – as per the (a), (b) and (c). There is an aesthetic appeal in having a position where there is only one solution. An analogy could be made to direct mate problems. It is this appeal that can override the concept of economy. Furthermore, a composer may wish that solutions are separated. This could be because two of say three are similar and the third, different – or because a sequence is desired. Some solvers may prefer the idea of finding one solution for each of two [different] positions – rather than two from one. It is not always possible for a composer to create separate solutions. (Author)

No.431 Peter Harris South Africa original – 23.11.2013 Dedicated to Thomas Maeder.   hs#5                                             (2+2) b) bKg7→c2; c) wKa8→c2 PWC Maximummer Transmuted Kings     Solutions: (click to show/hide)   a) 1.h7-h8=R Kg7xh8 [+wRg7] 2.Rg7-g2 Kh8-h7 3.Rg2xg8 [+bPg2] Kh7xg8 [+wRh7] 4.Rh7-c7 g2-g1=B 5.Ka8-b8 Bg1-a7 # b) 1.h7xg8=R [+bPh7] h7-h5 2.Rg8-g1 Kc2-d3 3.Rg1-h1 Kd3-e4 4.Rh1xh5 [+bPh1=bB] Bh1-f3 5.Rh5-h4 + Ke4-e8 # c) 1.h7xg8=Q [+bPh7] + Kg7-a1 2.Qg8-d5 h7-h5 3.Qd5xh5 [+bPd5] d5-d4 4.Kc2-c1 d4-d3 5.Qh5-f7 d3-d2 # (С+ by Popeye 4.63 and WinChloe 3.24)