Benko's Spring Cleaning Problems

GM Pal Benko presents some fun problems, as a complement to his April Chess Life Magazine problems. "Everybody likes to give checkmate, here you can solve 40 of them." The first part of these problems are more suitable for beginners or kids, and the second part of each are for more experienced solvers. 1.) How many mates in one are there? 
Show Solution
6! 1. Rde2#, 1. Rfe2#,  1.Ndc2# 1.Ndf5#, 1.Nfd5# 1. Nfg2#, Black's last move was e1=B.
81.B How many mates are there in 1 ?
Show Solution
Here it must be Black to move, because he had no possible last move.   There are four mates! 1...Bxc7  2.Rd7# or Re6#    1... Bxe7  2.R c6# or Rd7#
  2.)  The Black King dropped of the board Benko2 a) How many squares can we put the Black king on to have a mate in 1 ? Show Solution
 4!   Ka8,a6,f8,f6
b) Where we can put the Black King to have a mate in 2 ? White to play :Show Solution
 The king can go on e7 and then  1.a8N! and mate next move.
-------------------------------------------------------------------------------------------------- 3a.) Here the White Queen is missing. How many squares can we put the White Queen, so Black can mate in 1 two ways ? ( Helpmate in 1, Black to play , 2 solutions)
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5!  Qa3-e1-e2-e3-e4    1...Kf7 , or  1...0-0  
3b) From which of those squares can White helpmate Black in two in two different ways? (Helpmate in 2 , 2 solutions , Black to play)Show Solution
Qe4!     1...Kd7+  2.Kb7  Rd8  3.Qc6 mate   ,    1....Kd7+  2.Kb7 Re8  3. Qd5 mate
4.) Helpmate in 3 ( 2 solutions ). White to play.
Show Solution
1.g7  Kf7  2. Kh4  Kg6  3.gxh8N+  mate ,     1.gxf6 e.p.  0-0 2.f7+  Kh8  3. g7+ mate
---------------------------------------------------------------------------------- 5.) Benko5a) Check-mate in 2 to all the ten kings at the same time (Black to play) Show Solution
 1.Kd7  Bb5+  2. Kd6  Ne6+ mate
b) Check-mate in 3 to all the ten kings (White to  play ) Show Solution
 1.b8N!  Kc8  2. Ba6+  Kd8  3. Ne6+! mate

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