第 30878 題：含排固定物件的分割

原題與已知條件

相異標記物件無放回，有序與無序分開。n=20≥1、k=10、model=distinct_without_replacement，指定已存在標記0。求 (全組合數, 含0組合數, 排0組合數, 兩部分和減全數)。

• G001 — 相異標記物件無放回，有序與無序分開。n=20≥1、k=10、model=distinct_without_replacement，指定已存在標記0。求 (全組合數, 含0組合數, 排0組合數, 兩部分和減全數)。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-permutation-combination

逐步推導

source roles = [qf-density15-selection-one-distinguished-counts, density15_selection_one_distinguished_counts, finite_distinct_selection_protocol]

derived = [[total, included_label0, excluded_label0, partition_defect]]

Selection all subsets ordered ORIGINAL available-choice factor0 := mul(1, 20)

Selection all subsets ordered ORIGINAL available-choice factor0 = 20

Selection all subsets ordered ORIGINAL available-choice factor1 := mul(20, 19)

Selection all subsets ordered ORIGINAL available-choice factor1 = 380

Selection all subsets ordered ORIGINAL available-choice factor2 := mul(380, 18)

Selection all subsets ordered ORIGINAL available-choice factor2 = 6840

Selection all subsets ordered ORIGINAL available-choice factor3 := mul(6840, 17)

Selection all subsets ordered ORIGINAL available-choice factor3 = 116280

Selection all subsets ordered ORIGINAL available-choice factor4 := mul(116280, 16)

Selection all subsets ordered ORIGINAL available-choice factor4 = 1860480

Selection all subsets ordered ORIGINAL available-choice factor5 := mul(1860480, 15)

Selection all subsets ordered ORIGINAL available-choice factor5 = 27907200

Selection all subsets ordered ORIGINAL available-choice factor6 := mul(27907200, 14)

Selection all subsets ordered ORIGINAL available-choice factor6 = 390700800

Selection all subsets ordered ORIGINAL available-choice factor7 := mul(390700800, 13)

Selection all subsets ordered ORIGINAL available-choice factor7 = 5079110400

Selection all subsets ordered ORIGINAL available-choice factor8 := mul(5079110400, 12)

Selection all subsets ordered ORIGINAL available-choice factor8 = 60949324800

Selection all subsets ordered ORIGINAL available-choice factor9 := mul(60949324800, 11)

Selection all subsets ordered ORIGINAL available-choice factor9 = 670442572800

source roles = [Selection all subsets ordered, 20, 10]

derived = [[20, 19, 18, 17, 16, 15, 14, 13, 12, 11], 670442572800]

Selection all subsets within-subset ORIGINAL factorial factor2 := mul(1, 2)

Selection all subsets within-subset ORIGINAL factorial factor2 = 2

Selection all subsets within-subset ORIGINAL factorial factor3 := mul(2, 3)

Selection all subsets within-subset ORIGINAL factorial factor3 = 6

Selection all subsets within-subset ORIGINAL factorial factor4 := mul(6, 4)

Selection all subsets within-subset ORIGINAL factorial factor4 = 24

Selection all subsets within-subset ORIGINAL factorial factor5 := mul(24, 5)

Selection all subsets within-subset ORIGINAL factorial factor5 = 120

Selection all subsets within-subset ORIGINAL factorial factor6 := mul(120, 6)

Selection all subsets within-subset ORIGINAL factorial factor6 = 720

Selection all subsets within-subset ORIGINAL factorial factor7 := mul(720, 7)

Selection all subsets within-subset ORIGINAL factorial factor7 = 5040

Selection all subsets within-subset ORIGINAL factorial factor8 := mul(5040, 8)

Selection all subsets within-subset ORIGINAL factorial factor8 = 40320

Selection all subsets within-subset ORIGINAL factorial factor9 := mul(40320, 9)

Selection all subsets within-subset ORIGINAL factorial factor9 = 362880

Selection all subsets within-subset ORIGINAL factorial factor10 := mul(362880, 10)

Selection all subsets within-subset ORIGINAL factorial factor10 = 3628800

source roles = [Selection all subsets within-subset, 10]

derived = [3628800]

Selection all subsets ORIGINAL exact ordered over k factorial := div(670442572800, 3628800)

Selection all subsets ORIGINAL exact ordered over k factorial = 184756

Selection all subsets reverse unordered times k factorial := mul(184756, 3628800)

Selection all subsets reverse unordered times k factorial = 670442572800

source roles = [Selection all subsets, 20, 10, 670442572800, 3628800]

derived = [184756, 670442572800]

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor0 := mul(1, 19)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor0 = 19

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor1 := mul(19, 18)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor1 = 342

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor2 := mul(342, 17)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor2 = 5814

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor3 := mul(5814, 16)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor3 = 93024

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor4 := mul(93024, 15)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor4 = 1395360

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor5 := mul(1395360, 14)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor5 = 19535040

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor6 := mul(19535040, 13)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor6 = 253955520

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor7 := mul(253955520, 12)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor7 = 3047466240

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor8 := mul(3047466240, 11)

Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor8 = 33522128640

source roles = [Selection subsets INCLUDING label0 ordered, 19, 9]

derived = [[19, 18, 17, 16, 15, 14, 13, 12, 11], 33522128640]

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor2 := mul(1, 2)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor2 = 2

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor3 := mul(2, 3)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor3 = 6

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor4 := mul(6, 4)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor4 = 24

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor5 := mul(24, 5)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor5 = 120

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor6 := mul(120, 6)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor6 = 720

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor7 := mul(720, 7)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor7 = 5040

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor8 := mul(5040, 8)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor8 = 40320

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor9 := mul(40320, 9)

Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor9 = 362880

source roles = [Selection subsets INCLUDING label0 within-subset, 9]

derived = [362880]

Selection subsets INCLUDING label0 ORIGINAL exact ordered over k factorial := div(33522128640, 362880)

Selection subsets INCLUDING label0 ORIGINAL exact ordered over k factorial = 92378

Selection subsets INCLUDING label0 reverse unordered times k factorial := mul(92378, 362880)

Selection subsets INCLUDING label0 reverse unordered times k factorial = 33522128640

source roles = [Selection subsets INCLUDING label0, 19, 9, 33522128640, 362880]

derived = [92378, 33522128640]

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor0 := mul(1, 19)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor0 = 19

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor1 := mul(19, 18)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor1 = 342

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor2 := mul(342, 17)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor2 = 5814

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor3 := mul(5814, 16)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor3 = 93024

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor4 := mul(93024, 15)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor4 = 1395360

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor5 := mul(1395360, 14)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor5 = 19535040

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor6 := mul(19535040, 13)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor6 = 253955520

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor7 := mul(253955520, 12)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor7 = 3047466240

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor8 := mul(3047466240, 11)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor8 = 33522128640

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor9 := mul(33522128640, 10)

Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor9 = 335221286400

source roles = [Selection subsets EXCLUDING label0 ordered, 19, 10]

derived = [[19, 18, 17, 16, 15, 14, 13, 12, 11, 10], 335221286400]

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor2 := mul(1, 2)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor2 = 2

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor3 := mul(2, 3)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor3 = 6

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor4 := mul(6, 4)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor4 = 24

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor5 := mul(24, 5)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor5 = 120

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor6 := mul(120, 6)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor6 = 720

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor7 := mul(720, 7)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor7 = 5040

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor8 := mul(5040, 8)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor8 = 40320

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor9 := mul(40320, 9)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor9 = 362880

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor10 := mul(362880, 10)

Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor10 = 3628800

source roles = [Selection subsets EXCLUDING label0 within-subset, 10]

derived = [3628800]

Selection subsets EXCLUDING label0 ORIGINAL exact ordered over k factorial := div(335221286400, 3628800)

Selection subsets EXCLUDING label0 ORIGINAL exact ordered over k factorial = 92378

Selection subsets EXCLUDING label0 reverse unordered times k factorial := mul(92378, 3628800)

Selection subsets EXCLUDING label0 reverse unordered times k factorial = 335221286400

source roles = [Selection subsets EXCLUDING label0, 19, 10, 335221286400, 3628800]

derived = [92378, 335221286400]

Selection ORIGINAL included plus excluded := sum(92378, 92378)

Selection ORIGINAL included plus excluded = 184756

Selection ORIGINAL partition sum minus whole := sub(184756, 184756)

Selection ORIGINAL partition sum minus whole = 0

source roles = [20, 10]

derived = [184756, 92378, 92378, 0]

逐步反向核對

• S074 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S073 · premise_and_result_audit — 以精確有理數重算 Selection ORIGINAL partition sum minus whole，不以小數近似替代。
• S072 · premise_and_result_audit — 以精確有理數重算 Selection ORIGINAL included plus excluded，不以小數近似替代。
• S071 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S070 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 reverse unordered times k factorial，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ORIGINAL exact ordered over k factorial，不以小數近似替代。
• S068 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S067 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor10，不以小數近似替代。
• S066 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor9，不以小數近似替代。
• S065 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor8，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor7，不以小數近似替代。
• S063 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor6，不以小數近似替代。
• S062 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor5，不以小數近似替代。
• S061 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor4，不以小數近似替代。
• S060 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor3，不以小數近似替代。
• S059 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 within-subset ORIGINAL factorial factor2，不以小數近似替代。
• S058 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S057 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor9，不以小數近似替代。
• S056 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor8，不以小數近似替代。
• S055 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor7，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor6，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor5，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor4，不以小數近似替代。
• S051 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor3，不以小數近似替代。
• S050 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor2，不以小數近似替代。
• S049 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor1，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 Selection subsets EXCLUDING label0 ordered ORIGINAL available-choice factor0，不以小數近似替代。
• S047 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S046 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 reverse unordered times k factorial，不以小數近似替代。
• S045 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ORIGINAL exact ordered over k factorial，不以小數近似替代。
• S044 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S043 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor9，不以小數近似替代。
• S042 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor8，不以小數近似替代。
• S041 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor7，不以小數近似替代。
• S040 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor6，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor5，不以小數近似替代。
• S038 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor4，不以小數近似替代。
• S037 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor3，不以小數近似替代。
• S036 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 within-subset ORIGINAL factorial factor2，不以小數近似替代。
• S035 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S034 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor8，不以小數近似替代。
• S033 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor7，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor6，不以小數近似替代。
• S031 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor5，不以小數近似替代。
• S030 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor4，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor3，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor2，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor1，不以小數近似替代。
• S026 · premise_and_result_audit — 以精確有理數重算 Selection subsets INCLUDING label0 ordered ORIGINAL available-choice factor0，不以小數近似替代。
• S025 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S024 · premise_and_result_audit — 以精確有理數重算 Selection all subsets reverse unordered times k factorial，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ORIGINAL exact ordered over k factorial，不以小數近似替代。
• S022 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S021 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor10，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor9，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor8，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor7，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor6，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor5，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor4，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor3，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 Selection all subsets within-subset ORIGINAL factorial factor2，不以小數近似替代。
• S012 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。
• S011 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor9，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor8，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor7，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor6，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor5，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor4，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor3，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor2，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor1，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 Selection all subsets ordered ORIGINAL available-choice factor0，不以小數近似替代。
• S001 · premise_and_result_audit — 用原始資料、型別、索引與本步前提反向代回；一致性審查不等於可由結論唯一還原輸入。有限候選、獨立審查、形式證明與發布分開。

結論

(184756, 92378, 92378, 0)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。