2017 Christmas Theme Puzzles

Two Chrstmas-themed puzzles:

    • for the star on the left it is White to play and mate in 2
    • for the tree on the right it is Black to mate in 2.
Note: the puzzle on the right is significantly harder, and there are hints below.
Hint:
Spoiler: Highlight to view
What was White's previous move?
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Hint 2: 
Spoiler: Highlight to view
Count the number of captures the Black pawns made.
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Hint 3: 
Spoiler: Highlight to view
Where did White's Bishops go?
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Solutions: added Jan 1, 2018
 

Spoiler: Highlight to view

Red and Green Board: 1. Qe4 zugzwang. White has no mating threat, but any move allows mate in 1.
Wood Board: 
Solution: 1... bxc3 (ep) 2. (any move by the a or g pawns) ...c2#.
Explanation: This puzzle requires some retrograde analysis to deduce White's previous move.
  1. White's pawns on a2 and g2 have not moved, White's d5 pawn cannot have just moved since there are no empty squares behind it; there is no legal position from which White's last move could have been Kd1; this leaves only the c and e pawns as possible movers. They couldn't have moved from the third rank or the Kd4 would have been in check; so White's last move was either c2-c4 or e2-e4
  2. White has 6 pieces remaining of the original 16. So Black has captured 10 White pieces.
  3. Black's pawns have made 10 captures (all toward the center) to reach their current positions.
  4. Therefore, (2+3) all White pieces were captured by Black pawns.
  5. If White's last move was e2-e4 then the Bf1 would have been unable to move or be captured by a pawn and so would still be on f1.
  6. Black has already captured the f1 Bishop.
  7. Therefore, e2-e4 could not have been White's last move.
  8. Therefore, c2-c4 was White's last move.
 

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