小町表出問題

    *******
       ****
   12******
  **34****
  ***56**
******78   
*******90**

作者: 武純也氏
初出: こんわ会News 1982年10月号
再録: 虫食算パズル700選

以下のように記号を振る。

    abcdefg
       hijk
   12******
  **34****
  ***56**
******78   
*******90**

h,j,k>i。

fg×h=*78 となるものを探す。

39×2=078
89×2=178
26×3=078
13×6=078
63×6=378
54×7=378
42×9=378

これらに対し、h>i を考慮して defg×i=*56** となるものを探す。

5639×1=05639
5689×1=05689
5626×1=05626
2826×2=05652
7826×2=15652
5613×1=05613
2813×2=05626
7813×2=15626
5213×3=15639
1413×4=05652
3913×4=15652
6413×4=25652
8913×4=35652
5663×1=05663
8563×3=25689
5654×1=05654
8554×3=25662
5642×1=05642
2842×2=05684
7842×2=15684
8542×3=25626
0942×6=05652
5942×6=35652
2242×7=15694

まとめると以下のようになる。

56fg×1=056** fg=13,26,39,42,54,63,89
28fg×2=056** fg=13,26,42
78fg×2=156** fg=13,26,42
5213×3=156**
85fg×3=256** fg=42,54,63
1413×4=05652
3913×4=15652
6413×4=25652
8913×4=35652
0942×6=05652
5942×6=35652
2242×7=15694

acbdefg×k=12****** となる abcdefg の範囲を探す。

6000000–6499999×2=12000000–12999998
4000000–4333333×3=12000000–12999999
3000000–3249999×4=12000000–12999996
2400000–2599999×5=12000000–12999995
2000000–2166666×6=12000000–12999996
1714286–1857142×7=12000002–12999994
1500000–1624999×8=12000000–12999992
1333334–1444444×9=12000006–12999996

abcdefg×j=**34**** となる j の値を探す。

6170000–6174999×2=12340000–12349998
6113334–6116666×3=18340002–18349998
6446667–6449999×3=19340001–19349997
6085000–6087499×4=24340000–24349996
6335000–6337499×4=25340000–25349996
6068000–6069999×5=30340000–30349995
6268000–6269999×5=31340000–31349995
6468000–6469999×5=32340000–32349995
6056667–6058333×6=36340002–36349998
6223334–6224999×6=37340004–37349994
6390000–6391666×6=38340000–38349996
6048572–6049999×7=42340004–42349993
6191429–6192857×7=43340003–43349999
6334286–6335714×7=44340002–44349998
6477143–6478571×7=45340001–45349997
6042500–6043749×8=48340000–48349992
6167500–6168749×8=49340000–49349992
6292500–6293749×8=50340000–50349992
6417500–6418749×8=51340000–51349992
6037778–6038888×9=54340002–54349992
6148889–6149999×9=55340001–55349991
6260000–6261111×9=56340000–56349999
6371112–6372222×9=57340008–57349998
6482223–6483333×9=58340007–58349997
4113334–4116666×3=12340002–12349998
4085000–4087499×4=16340000–16349996
4068000–4069999×5=20340000–20349995
4268000–4269999×5=21340000–21349995
4056667–4058333×6=24340002–24349998
4223334–4224999×6=25340004–25349994
4048572–4049999×7=28340004–28349993
4191429–4192857×7=29340003–29349999
4042500–4043749×8=32340000–32349992
4167500–4168749×8=33340000–33349992
4292500–4293749×8=34340000–34349992
4037778–4038888×9=36340002–36349992
4148889–4149999×9=37340001–37349991
4260000–4261111×9=38340000–38349999
3085000–3087499×4=12340000–12349996
3068000–3069999×5=15340000–15349995
3056667–3058333×6=18340002–18349998
3223334–3224999×6=19340004–19349994
3048572–3049999×7=21340004–21349993
3191429–3192857×7=22340003–22349999
3042500–3043749×8=24340000–24349992
3167500–3168749×8=25340000–25349992
3037778–3038888×9=27340002–27349992
3148889–3149999×9=28340001–28349991
2468000–2469999×5=12340000–12349995
2556667–2558333×6=15340002–15349998
2477143–2478571×7=17340001–17349997
2417500–2418749×8=19340000–19349992
2542500–2543749×8=20340000–20349992
2482223–2483333×9=22340007–22349997
2593334–2594444×9=23340006–23349996
2068000–2069999×5=10340000–10349995
2056667–2058333×6=12340002–12349998
2048572–2049999×7=14340004–14349993
2042500–2043749×8=16340000–16349992
2037778–2038888×9=18340002–18349992
2148889–2149999×9=19340001–19349991
1723334–1724999×6=10340004–10349994
1762858–1764285×7=12340006–12349995
1792500–1793749×8=14340000–14349992
1815556–1816666×9=16340004–16349994
1620000–1621428×7=11340000–11349996
1542500–1543749×8=12340000–12349992
1593334–1594444×9=14340006–14349996
1417500–1418749×8=11340000–11349992
1371112–1372222×9=12340008–12349998

abcdefg×i=7桁を考慮して上3桁と下4桁を組み合わせる。

61156fg×h132 fg=13,26,39,42,54,63,89 h=6,3,2,9,7,6,2
60856fg×h142 fg=13,26,39,42,54,63,89 h=6,3,2,9,7,6,2
63356fg×h142 fg=13,26,39,42,54,63,89 h=6,3,2,9,7,6,2
63356fg×h172 fg=13,26,39,42,54,63,89 h=6,3,2,9,7,6,2
41156fg×h133 fg=13,26,42,54,63 h=6,3,9,7,6
40856fg×h143 fg=13,26,42,54,63 h=6,3,9,7,6
40578fg×h263 fg=13,26,42 h=6,3,9
41928fg×h273 fg=13,26,42 h=6,3,9
40428fg×h283 fg=13,26,42 h=6,3,9
41678fg×h283 fg=13,26,42 h=6,3,9
42928fg×h283 fg=13,26,42 h=6,3,9
40378fg×h293 fg=13,26,42 h=6,3,9
30856fg×h144 fg=13,42,54,63 h=6,9,7,6
3085213×6344
30685fg×h354 fg=42,54,63 h=9,7,6
30578fg×h264 fg=13,42 h=6,9
31928fg×h274 fg=13,42 h=6,9
30428fg×h284 fg=13,42 h=6,9
31678fg×h284 fg=13,42 h=6,9
31685fg×h384 fg=42,54,63 h=9,7,6
30378fg×h294 fg=13,42 h=6,9
30385fg×h394 fg=42,54,63 h=9,7,6
24685fg×h355 fg=42,54,63 h=9,7,6
2468913×6455
25578fg×h265 fg=13,42 h=6,9
24778fg×h275 fg=13,42 h=6,9
24785fg×h375 fg=42,54,63 h=9,7,6
24178fg×h285 fg=13,42 h=6,9
24185fg×h385 fg=42,54,63 h=9,7,6
25428fg×h285 fg=13,42 h=6,9
24828fg×h295 fg=13,42 h=6,9
20685fg×h356 fg=42,54,63 h=9,7,6
2068913×6456
20578fg×h266 fg=13,42 h=6,9
2048913×6476
20428fg×h286 fg=13,42 h=6,9
20378fg×h296 fg=13,42 h=6,9
20385fg×h396 fg=42,54,63 h=9,7,6
2148913×6496
1723913×6467
1763913×6477
17928fg×h287 fg=13,42 h=6,9
18156fg×h197 fg=13,42,54,63 h=6,9,7,6
1816413×6497
1620942×9678
1621413×6478
1542842×9288
1593913×6498
1417842×9289
14185fg×h389 fg=42,54 h=9,7

efg×ijk=***0*** となるものを探し、abcdefg×hijk を計算する。

6085613×6142=37377835046
6335613×6142=38913335046
6335663×6172=39103712036
4042813×6283=25400994079
4167813×6283=26186369079
4292813×6283=26971744079
4037826×3293=13296561018
3037813×6294=19119995022

90が現れるのは1つなのでこれが解である。

解答
4167813 6283 12503439 33342504 8335626 25006878 26186369079

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