No. of units A B C D E F
2            
3   1 1      
4   2 3     1
5   3       2
6   4       3
7 1   6      
8 2 5(Cx) 7 1    
9   7        
10     8 2    
11 3 8(C) 9      
12 5          
13            
14 6 10(C) 11      
15         1  
16   11(C) 12      
17       3    
18 16 16(A) 16(A)      
19            
20            
21            
22       15    
23     24      
24 20 20(A) 29     11
25 28 28(A,Cx) 37      
26 96 96(A) 96(A)   4  
27            
28            
29         12 19
30         22  
31            
32            

Length records in "Last N single moves?" problems

compiled by Thierry Le Gleuher & Alain Brobecker, march 2007

This page shows retrograde analysis problems where the solver is asked to find the last N single moves played to reach the position.  The design objective is to maximize N and minimize the total number of units, M. Records are positions where one can improve neither of M or N, without worsening the other.

This is an extension of the "Last move" task, discussed in several webpages. Records are classified in the following six categories:

The number in the first column is M. Then there is one column per problem type, T. The non-blank cells show the records: the cell (M, T) contains the value of N.

When a record also applies to a less restrictive type, then the cell instead contains the letter referring to the least restrictive type.

In some cases, a record for Type C, apart from the last move, can also apply as a record for Type B: this is denoted C or Cx depending on whether the last move was a capture.

The problems here are also available from Alain as a pdf.



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