## Last Move problems

In the various types of Last Move problem, the composer's game is to find diagrams which uniquely determine what was the last move. What unit moved from what square to what square, and what did it capture if anything. Five types are discussed here:

• Type A: It is not given who has the move. Neither king is in check.
• Type B: The stipulation says who has the move. Neither king is in check.
• Type C: One king is in check.[1]
• Type D: Duplex.
• Type F: Colouring problem - one king may be in check.

For any particular type, composers have tried to find minimal diagrams for 60 different tasks:

• unit type X has just moved without capture (6 cases, corresponding to the 6 unit types)
• unit type X has just captured unit type Y (6x5 = 30 cases)
• pawn has just promoted without capture, to unit type Z (4 cases)
• pawn hast just captured unit type Y on the back rank, promoting to unit type Z (5x4 = 20 cases)
• double pawn move or en passant capture (2 cases)
• king's side or queen's side castling (2 cases).

Any Type A position can appear as a valid Type B position. It follows that the Type A record for any task must be greater than or equal to the Type B record.

In 1978, A.S.M.Dickins defined minimality for this task [2]:

1. smallest number of units
2. where the number of units is equal, the smallest number of pieces (as opposed to pawns),
3. where the number of units and pieces is the same, the smallest number of major pieces.

The final tiebreaker is the date of publication.

The use of evidently promoted material (e.g. two dark-squared White bishops) is not an factor in grading these positions, although a composer may avoid this if possible.

These tasks have been around since at least 1924 and many of the problem greats have turned their hand to them. It is hard to improve on the established records. Looking at the dates of the problems, it appears that progress has come in waves over the decades. The most recent surge (2007, Type D) explores the duplex stipulation.

A handful of the records are impacted by the arrival of Dead Reckoning in 1997. This has slightly changed the rules, so it seems fairest and most interesting to keep both the old and the new records.

[1] Prior to June 2007, the check was optional. However this was confusing and made very little difference. See Werner Keym, Die Schwalbe, Heft 225, June 2007, p.143-145.

[2] Die Schwalbe, Heft 51, June 1978, p.245.