Bidirectional Cycle (XY-Cycle)

The cells D9, F8, H8, H3, E3 and D2 form a bidirectional cycle: there are exactly two ways of placing the values in these cells, forming two different possible configurations. Some values appear in a row, column or box regardless of which configuration is correct. Because one of the two configurations must be correct, other occurrences of these values can be removed from these rows, columns or boxs.

The two configurations of the bidirectional cycle are enforced by two complementary, circular chains of implications. The details of each chain are given below.

Cycle details, forward direction (View 1):
(1) If D2 contains the value 7 then D9 cannot contain the value 7 (the value can occur only once in the col)
(2) If D9 does not contain the value 7 then D9 must contain the value 5 (only remaining potential value in the cell)
(3) If D9 contains the value 5 then F8 cannot contain the value 5 (the value can occur only once in the box)
(4) If F8 does not contain the value 5 then H8 must contain the value 5 (only remaining position in the row)
(5) If H8 contains the value 5 then H3 cannot contain the value 5 (the value can occur only once in the col)
(6) If H3 does not contain the value 5 then H3 must contain the value 7 (only remaining potential value in the cell)
(7) If H3 contains the value 7 then E3 cannot contain the value 7 (the value can occur only once in the row)
(8) If E3 does not contain the value 7 then D2 must contain the value 7 (only remaining position in the box)

Cycle details, reverse direction (View 2):
(1) If D2 does not contain the value 7 then E3 must contain the value 7 (only remaining position in the box)
(2) If E3 contains the value 7 then H3 cannot contain the value 7 (the value can occur only once in the row)
(3) If H3 does not contain the value 7 then H3 must contain the value 5 (only remaining potential value in the cell)
(4) If H3 contains the value 5 then H8 cannot contain the value 5 (the value can occur only once in the col)
(5) If H8 does not contain the value 5 then F8 must contain the value 5 (only remaining position in the row)
(6) If F8 contains the value 5 then D9 cannot contain the value 5 (the value can occur only once in the box)
(7) If D9 does not contain the value 5 then D9 must contain the value 7 (only remaining potential value in the cell)
(8) If D9 contains the value 7 then D2 cannot contain the value 7 (the value can occur only once in the col)