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I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found this quite simple algorithm (which has two cases, either it is a row change [type2] or not [type1]):

 Type 1:
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last row up
 Type 2, row change:
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

Edit: The solution at @Daedric's link seems to be unnessarily complex...

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found this quite simple algorithm (which has two cases, either it is a row change [type2] or not [type1]):

 Type 1:
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last column upwards
 Type 2, row change:
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found this quite simple algorithm (which has to cases, either it is a row change [type2] or not [type1]):

 Type 1:
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last row up
 Type 2, row change:
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

Edit: The solution at @Daedric's link seems to be unnessarily complex...

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found this quite simple algorithm (which has two cases, either it is a row change [type2] or not [type1]):

 Type 1:
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last row up
 Type 2, row change:
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

Edit: The solution at @Daedric's link seems to be unnessarily complex...

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found that this quite simple algorithm (which has to cases, either it is a row change [type2] or not [type1]):

 REPEAT 2 (type 1)
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last row up
 REPEAT 1 (type 2, row change)
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

Edit: The solution at Daedric's link seems to be unnessarily complex...

I mapped the symbols to $\{0,1,2\}$, so we get:

 011 | 221 | 022
 001 | 120 | 011
 222 | 001 | 120
-----------------
 210 | 210 | 210
 212 | 201 | 122
 001 | 120 | 010
-----------------
 020 | 012 |
 121 | 020 |  ?
 210 | 211 |

I found this quite simple algorithm (which has to cases, either it is a row change [type2] or not [type1]):

 Type 1:
 * we (+1 mod 3) every element 
 * rotate columns left one step
 * rotate last row up
 Type 2, row change:
 * rotate the matrix 90 degrees

Since the final step is type 1, we get

 120      120      120
 200  ->  200  ->  202
 112      112      110

and then +1 and translate back to cardsymbols.

 120      201       ♥♦♣
 202  --> 010  -->  ♦♣♦
 110      221       ♥♥♣

I don't know about the discrepancy. The first and wrong matrix does not make sense to me.

Edit: The solution at @Daedric's link seems to be unnessarily complex...