【へやわけ】角5x48に黒マスが87個しか入らないこと

超超へやわけMX：

https://scrapbox.io/nishinanntoka/%E8%B6%85%E8%B6%85%E3%81%B8%E3%82%84%E3%82%8F%E3%81%91MX

 

コンピューターを用いた探索により、$L$ が小さい場合に角 $5\times L$ に入る黒マスの最大値が求められている。

https://scrapbox.io/nishinanntoka/%E3%81%B8%E3%82%84%E3%82%8F%E3%81%91DP

以下は一般の $L$ についての結果を考察したもの。$L = 16m$ と表される場合について、タイトな上界を求める。

 

続きを読む

WPC選抜2022問題のツール起し

 

1 arithmetic square

https://opt-pan.github.io/penpa-edit/?m=solve&p=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

 

2 letter weights

https://opt-pan.github.io/penpa-edit/?m=solve&p=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

 

3 scrabble

省略

 

4 Tapa 10+30

https://puzz.link/p?tapa/9/9/3h3h4p2oa7gbngbng9ga7zbmgafhaaq4m

https://puzz.link/p?tapa/12/12/ma9k5hafkalnafnbnnafkaehalkaltbqk3hbnkalnbqnaln4kafhaaka8m

 

5 pentominous 14+22

https://opt-pan.github.io/penpa-edit/?m=solve&p=1ZFNTsMwEIX3PsasvfDEdpp4C3RVVag/KsWyEAsOAIiNo/bsHT8kMs0NkOMv0Zd5T5Hz/fnz/vVh2bXLD1busgIP2N3Qt22ykxeyisnUkcVmKte6v2Yiy8VMdZem+pZyudh6nB/3aRJu00Q+UMr0LNPIWvKxiaMSQxNrJcZFJKBDRQI6zrNYLSOjW0RG38RpFuy6Zl60Qa36EuZ+0csRxa/acDMbbZC6M6tmDsr06Nlqg56/GTk/ximewTXYgQc5ZFs9+Ag6MIIbzDyBJ/ABDMKLMdn//uz7Ff+fKzc=

https://opt-pan.github.io/penpa-edit/?m=solve&p=1ZHPTgQhDIfvPEbPHCh/RuSqbmJi9uC6blZCjAcfQI0XyO6zT/mZCOoTmE6/mXyUDp35ePt8eX/VbPrlopa7hOeItHHpqbKRBYmiMlnSSKZyrrtzJtJcVKv3qdXnlMtJ1/143KUm3KZGzlDK9CjV2KvJ+S72Q/jQxXESl11shgjcxWGIZeliO8QFetwOEeMvwQYlU1e2ONrUha37U4M+0+HY4d1Pk/HY9T2RDM4Y/whuQAs+yNfR1YHXoAEDeIeaG/AAXoFeeFIqu6+/9DPC/3NlBQ==

 

6 kropki 14+27

https://puzz.link/p?kropki/6/6/0009300009687c31116d

https://puzz.link/p?kropki/6/6/0009300009687c31126d

 

7 hashi 16+31

https://puzz.link/p?hashi/10/10/2i3i2h2g4h5h24g2h2g1n2g1h1g4g3g2g25g2g3i4h2g3h1h32l2i2h4g2g2g3h3g3g5g3

https://puzz.link/p?hashi/12/12/2g4i3h2g2i2g3g4h3i1g1g1j24h2g1g2g1j1g4g3g2g3h2g3g2g2g3g34g2g1g1g2j1g3g4g3h2i2g2g3g3j2g2g1g2g2g31g2g3g3g3g2h2i2g3i2

 

8 tents 18+38

https://puzz.link/p?tents/9/9/g3k2g22k14462442c32036630231

https://puzz.link/p?tents/10/10/g2i2i2g23i23hj42655137a1136042200d10

 

9 snake 16+32

https://puzz.link/p?snake/10/10/00000000200000000000000000000i0000634i74g4i5h6226

https://puzz.link/p?snake/10/10/0000000200000000000000002000000000h5h3g2h54h23h3g

 

10 skyscrapers 22+39

https://puzz.link/p?skyscrapers/6/6/g3g4j3g4h24h52h42g

https://puzz.link/p?skyscrapers/7/7/g432l456g3h234h432h2

 

11 yin-yang 16+52

http://pzv.jp/p.html?yinyang/9/9/0001693f630i18009i3f6169900

http://pzv.jp/p.html?yinyang/12/12/ddddf07p03i110c1k007i404j547i0k1i96ii039mla5qqqq

 

12 fillomino 18+50

https://puzz.link/p?fillomino/9/9/h3k3g1j36h4g35i3i2g21h2m1h12g2i1i51g2h52j3g2k3h

https://puzz.link/p?fillomino/12/12/h3h2g5j1h1g1g9g1513g3p1g69g2g361m1k2g3g1h6g2g77g4g3h1g3g4k4m124g1g15g1p1g4173g2g2g1h2j4g4h4h

 

13 starbattle 19+48

https://puzz.link/p?starbattle/9/9/2/ga9jr6e3j7e4j10e2qhjhm3ced2p3g

https://puzz.link/p?starbattle/11/11/2/k8ac8pk5ueues46but2o4ga3gpiv0n4001q4vacioc4f

 

14 easy as ABC 23+50

https://puzz.link/p?easyasabc/6/6/3/g3g22h12g3h11g1h3g33g

https://puzz.link/p?easyasabc/8/8/5/g3111g32g2g333i1g4441i222g31

 

15 four winds 18+60

https://puzz.link/p?walllogic/8/8/h4j4j6i4g1i5k2l3k5i1g2i4j4j5h

https://puzz.link/p?walllogic/10/10/h2i3h4g2i3m3j5g4i4h2i1j3l3j1i2h4i3g4j5m3i4g3h5i3h

 

16 battleships 18+50

https://opt-pan.github.io/penpa-edit/?m=solve&p=1VS7autAEO31GVtPMbMvrVTmVYUU8Q0hCGEcMCSQIomdRsL+ds9METvS6AMuQgdxzrz27Ni7r5/N9xaIgBKEAgj8BTFlyFiAope36pAFfvqqc+TAeX7J9cdhdeycA+qrcXhsx2Hddv0Bhqfz56odGR/a0aXatZ1kkuaCq70QeCbKNIJQQy6ZoEy6YPIsptY6POcvU8I0psRJcyppFpNnTJl2b3Aa09Cf7nx6Ug9e2IPQsBbBvW72+4/t7u39c33lwHNaI5VrSyGU42RTakQKtiQFvS3JFKbkUY6TTInEZ7OXJ7HXLkjis13QLw7vvQxvZ+kC2FlBxrCzomTxhViS3LspsfNih+0v1nLPtsGoq21OQqibt1BTd3AhTy/UnpNQZjE0Xrs7XT6v+I9/kzAExRtFVEyK9xpzq/iseK0YGQ9V1QX+L5g9+f/j+hM=

https://opt-pan.github.io/penpa-edit/?m=solve&p=1VM9a8NADN39M27WIOnu4ovHfk2lQ9NSymFCCoEWOrRNutgkvz2SlqSJ/AOK8cO8d9I9fXjz/bv6WQMRUIZYAEG+IOUZzLAAJda3qSiCPH1TAwUILC+Ffj8s9jUEoL4Zh8duHJZd7XcwPB8/F90o+NCNIbehqxpJFguhnBOErEw6YcjOnDLJmHjClKiM2Doy6TxzyRdR5YKZnzNz+pNZCiEr51XKSXo6Q3hbbbef6837x9fyKgCbaS0judJc3UdfUkPsS3qXKzHilA02G+5dTNoyPyFp7/yEPGmeWc37UXHaRlQbflTSKGm7J+ksXYmw1Xb4/cVWp+k3GFu9zp8m2jZN5LS9moizgfo+CdWLo8ly3dmKseGT/EQwRMMbQzTMhvd25tbwxfDaMAnumqZG+Xkvntn/4/oD

 

17 masyu 16+55

https://puzz.link/p?mashu/10/10/30033096103210100a0i00009ii9900010

https://puzz.link/p?mashu/12/12/033919100199c90100242200099010029090630i90010bj0

 

18 nurikabe 31+55

https://puzz.link/p?nurikabe/10/10/5g2g1r3n3l2q2i5h1j2i3r3k5j3g4r

https://puzz.link/p?nurikabe/16/16/h4v4m1l4i5k1p5i1p5zg8t8l3o8j3g3zp2n7g7i2p7k2y6t6g6zj

 

19 magnets 30+40

https://opt-pan.github.io/penpa-edit/?m=solve&p=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

https://opt-pan.github.io/penpa-edit/?m=solve&p=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

 

20 coral 15+67

https://opt-pan.github.io/penpa-edit/?m=solve&p=vZK9bsMwDIR3PYZmDqZoyarW/kxFhv6gKAyh6NAHaIMuMpJnD30BGoXeC5sf5PMdCdDef/9+/nwR83pLpoH0RGNMKOawlptFX2hVN3v25IMW+3psuyOEUN3SnsrSPspcD9ReL8fnsih3ZfGSfIGbESYf2QqyCtIJiOi0P2EykRRXIXWCjaRsmk4YO3ZCME0nRLoe040ReLAWHuDp5rBsPLLpE+1sPi/hShmtkjeefO3RlTMW/w4+gAF80e9CTcA7cAAj+AjPPfgG3oKj8uDcnM8/yOXK//tcTw==

https://opt-pan.github.io/penpa-edit/?m=solve&p=1ZI9bsMwDIV3HUOzBpGiE0Vrf6YiQ39QFIJRdOgB0qKLjOTsoZ+BVuINCpkPxmdK1KP5ffr5+PoMlNYn5RAD6ZoSI0hkDVeTftCYXfXkg2cN8vOlHS8APLulPZalvZc6n0N7+Xt9KovqsSxeki913UrYHLzsDZh2FmQDdtECXoFe4ReIydijrHRgshm4R+rAwWRkMhkZZTtAEacOBG56kqwdSrYSiXVIm4GBwGNnibdaXRs4wtRAbHVmezKz7R6z7RZvN+xPFrRnIONv0QkgzMEb9B7K0Gcdk9AS9BYaoRP0ATl30FfoDVRUz87Vwzav48r/j81X

 

21 slitherlink 13+71

https://puzz.link/p?slither/9/9/g8c678a8bh1bg3di3bg21cg2bi0cg3dh7b687d7d

https://puzz.link/p?slither/12/12/2777863266bm771131216338bo02827abi3cib63712bo601512132256bm5521886773b

 

22 galaxies 25+70

https://puzz.link/p?tentaisho/10/10/znejemenej6ezeiezietceleziekezzgeg6ejeney

https://puzz.link/p?tentaisho/10/10/heoeew4ezzt82ezzzg8ezp88ezzuelexege

 

23 kakkuro 22+91

https://puzz.link/p?kakuro/9/9/nD--DrbCm-4lagng-6-ECnfhp7fp6bnD-.4gnhblg-m-Gr.-Jnh9BgBGgAOC367

https://puzz.link/p?kakuro/12/12/a-fGo-bmD-qOgqP4l9blagneAoAeqBUqi-THnBblb5nb9l9dng-K-qbJqjgoe8n7hlc5l6Bq-Kq-9m-ho..65BCeC4KJ78ggVd6I

 

 

 

自作バトルシップ解説

最近作問した高難易度のバトルシップについて、解説を載せます。

6 問作成しましたが、根底にある考え方は同じなので、その中から 1 つ選んで解説します。解説するのは 4 つ目に出した次の問題です：

f:id:SP1_puzzle:20210813140744p:plain

ツール・解答登録のリンク

 

一見すると何の手掛かりもないように見えますが、裏に隠された制約を見破ることでロジカルに解答を導くことができます。以下の解説ではその制約の説明をしたあと、実際に正解までの手順を追っていくことにします。

 

なお、他の問題もあわせてリンクを貼っておきます。

1 問目 8x8

2 問目 8x8

3 問目 10x10, 2 問目の拡張

4 問目 10x10, 上のもの、1 問目の拡張

5 問目 8x8

6 問目 8x8, 5 問目の拡張

 

続きを読む