No, kiszámoltam kimerítő kereséssel, és 20 lehetőség jött ki.
Érdekes módon egyetlen olyan felosztás sincsen, amiben hat új megye keletkezik három-három régiből, és egy régi egyedül marad.
Itt van az összes (értelmes sorrend nélkül).
{{K, L}, {N, R}, {A, B, C}, {O, P, S}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{K, L}, {P, S}, {A, B, C}, {N, O, R}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{K, N}, {L, P}, {A, B, C}, {O, R, S}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{K, N}, {P, Q}, {A, B, C}, {O, R, S}, {D, G, H}, {E, F, J}, {I, L, M}},
{{K, N}, {R, S}, {L, O, P}, {A, B, C}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{L, P}, {R, S}, {K, N, O}, {A, B, C}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{A, C}, {K, N}, {M, P, Q}, {B, D, G}, {O, R, S}, {E, F, J}, {H, I, L}},
{{A, C}, {N, R}, {B, D, G}, {O, P, S}, {E, F, J}, {H, K, L}, {I, M, Q}},
{{A, C}, {P, S}, {B, D, G}, {N, O, R}, {E, F, J}, {H, K, L}, {I, M, Q}},
{{A, C}, {R, S}, {K, N, O}, {M, P, Q}, {B, D, G}, {E, F, J}, {H, I, L}},
{{N, R}, {P, S}, {K, L, O}, {A, B, C}, {D, G, H}, {E, F, J}, {I, M, Q}},
{{D, G}, {K, N}, {A, B, C}, {M, P, Q}, {O, R, S}, {E, F, J}, {H, I, L}},
{{D, G}, {N, R}, {A, B, C}, {O, P, S}, {E, F, J}, {H, K, L}, {I, M, Q}},
{{D, G}, {P, S}, {A, B, C}, {N, O, R}, {E, F, J}, {H, K, L}, {I, M, Q}},
{{D, G}, {R, S}, {K, N, O}, {A, B, C}, {M, P, Q}, {E, F, J}, {H, I, L}},
{{P, Q}, {R, S}, {K, N, O}, {A, B, C}, {D, G, H}, {E, F, J}, {I, L, M}},
{{I, L}, {K, N}, {A, B, C}, {M, P, Q}, {O, R, S}, {D, G, H}, {E, F, J}},
{{I, L}, {R, S}, {K, N, O}, {A, B, C}, {M, P, Q}, {D, G, H}, {E, F, J}},
{{I, Q}, {K, N}, {L, M, P}, {A, B, C}, {O, R, S}, {D, G, H}, {E, F, J}},
{{I, Q}, {R, S}, {K, N, O}, {L, M, P}, {A, B, C}, {D, G, H}, {E, F, J}},
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