This page contains all moves up to ply 10 that determine all the previous moves uniquely and depend on SAN disambiguation. The list of moves beyond ply 10 is possibly incomplete. Remember that in SAN, ambiguities are resolved by specifying the file, and if this fails, the rank instead. For example, if the problem says "Raxa3", then there must be a second rook capable of capturing the piece on a3 to justify the disambiguation.
This is very weird and I'd be interested to know about any other chess problem of any type which depends on SAN disambiguation.
SAN (Standard Algebraic Notation) is the notation used in most modern chess publications and in PGN files. For a mathematically precise definition of SAN, see the Portable Game Notation Specification, Section 8.2.3.
4... Raxa3
4... Raxa4 (similar to Raxa3)
4... Rhxa3 (similar to Raxa3)
4... Rhxa4 (similar to Raxa3)
5. Rcxa6
5. Rdxa5 (similar to Rcxa6)
5. Rdxa6 (similar to Rcxa6)
5. Rexa5 (similar to Rcxa6)
5. Rexa6 (similar to Rcxa6)
5. Rfxa5 (similar to Rcxa6)
5. Rfxa6 (similar to Rcxa6)
5. Rgxa5 (similar to Rcxa6)
5. Rgxa6 (similar to Rcxa6)
5... N4c6#
5... N8c6# (similar to N4c6#)
5... N8h6#
5... Ndc6#
7. B2g5# (published in The Problemist, 03/2016)
7. B2a5# (similar to B2g5#)
7. Q1xc7# (published in The Problemist, 03/2016)
7... Q1c1# (published in The Problemist, 03/2016)
7... Q8xb2# (published in The Problemist, 03/2016)
8. Qaxc2# (published in The Problemist, 03/2016)
8. Qfa6# (published in The Problemist, 03/2016)
8. Qfxa6# (similar to Qfa6#)