tag:blogger.com,1999:blog-3550204829234352390.post7545336730390170274..comments2024-02-10T19:14:35.934+08:00Comments on 研發養成所 ( Bridan's Blog - 4rdp, For R&D Person ): 訓練數學感 87 ─ 四子三連線Bridanhttp://www.blogger.com/profile/17055047757114667099noreply@blogger.comBlogger26125tag:blogger.com,1999:blog-3550204829234352390.post-82993770872643064672016-08-05T23:57:45.902+08:002016-08-05T23:57:45.902+08:00您的觀察是正確的,https://oeis.org/A273916/a273916.png,目前需要...您的觀察是正確的,https://oeis.org/A273916/a273916.png,目前需要補充的是 16 連線以上,謝謝Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-13460272691224723972016-08-05T23:43:50.864+08:002016-08-05T23:43:50.864+08:00偶然看見這個題目.發現
四子三連線 之 六連線還可以https://www.desmos.com/...偶然看見這個題目.發現 <br />四子三連線 之 六連線還可以https://www.desmos.com/calculator/eqzyaq0v4b <br /> 12子Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-45167644336235791822016-02-26T22:51:55.813+08:002016-02-26T22:51:55.813+08:00X X X X o X X X X o X X X X
X X X X o X X X X o X ...X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X X<br />X X X X X X X X X X X X X X X<br />依據老師畫的圖的上半部(在此我只有討論上半部)<br />4,7,9,11,12,13,14,15,16,16,18,<br />21,24,26,28,30,31,32,32,33,34,35,<br />38,41,43,45,47,48,49,49,50,51,52,<br />55,58,60,62,64,65,66,66,67,68,69,...<br />第一行有點不同,二行開始照規律持續下去<br /><br />.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-88259384376593793862016-02-26T21:04:35.019+08:002016-02-26T21:04:35.019+08:00老師謝謝你,看懂你的圖了,我不確定這是否為最佳連圖,如果是,那確實可以無限相連。老師謝謝你,看懂你的圖了,我不確定這是否為最佳連圖,如果是,那確實可以無限相連。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-10118415432307486452016-02-26T18:32:55.690+08:002016-02-26T18:32:55.690+08:00按4,7,9,11,12,13,14,15,16,16,18 搜索,OEIS確實沒有這個數列。按4,7,9,11,12,13,14,15,16,16,18 搜索,OEIS確實沒有這個數列。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-88927982756056778482016-02-26T18:16:34.698+08:002016-02-26T18:16:34.698+08:00這是一幅可以無限擴展的圖,所有最少子的連線圖,應該都可以從中找出來。這是一幅可以無限擴展的圖,所有最少子的連線圖,應該都可以從中找出來。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-6483061084672566432016-02-26T18:13:11.552+08:002016-02-26T18:13:11.552+08:00終於排好了,X表示要下棋子的地方,o表示留空的地方。終於排好了,X表示要下棋子的地方,o表示留空的地方。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-44082857698817079652016-02-26T18:12:12.805+08:002016-02-26T18:12:12.805+08:00X X X X o X X X X o X X X X
X X X X o X X X X o X ...X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X X<br />X X X X X X X X X X X X X X<br />X o o o o o o o o o o o o o <br />X X X X X X X X X X X X X X<br />X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X X<br />X X X X o X X X X o X X X Xflyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-10329287706596412302016-02-24T21:22:06.768+08:002016-02-24T21:22:06.768+08:00老師您的圖,我看不懂意思,有空再補充說明,謝謝。老師您的圖,我看不懂意思,有空再補充說明,謝謝。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-59728187410658384702016-02-24T21:21:34.881+08:002016-02-24T21:21:34.881+08:00如果有禁手並可連子,依據你排列方式,十一連線 18 子應該是最少。如果有禁手並可連子,依據你排列方式,十一連線 18 子應該是最少。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-26615585043844881472016-02-24T20:35:06.916+08:002016-02-24T20:35:06.916+08:00請問十一連線是18子嗎?
XXXXXX
.XXXX
.XXXX
.XXXX請問十一連線是18子嗎?<br />XXXXXX<br />.XXXX<br />.XXXX<br />.XXXX.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-71891265265114066472016-02-24T20:24:09.534+08:002016-02-24T20:24:09.534+08:00作者已經移除這則留言。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-81118693669131331372016-02-24T17:00:31.282+08:002016-02-24T17:00:31.282+08:00雖然禁手使得相連的兩個矩陣少了兩條線(因為禁手算0條),但同時也增加了兩條!故實際連線數並未減少。
...雖然禁手使得相連的兩個矩陣少了兩條線(因為禁手算0條),但同時也增加了兩條!故實際連線數並未減少。<br />相反,從第三個矩陣開始,每多一個矩陣,都可以從原本已經是禁手的連線中多獲得1條線!(如圖)<br />X X X X X X X X X X X X<br />X X X X X X X X X X X X<br />X X X X X X X X X X X X<br />X X X X x X X X X x X X X X<br />x <br />X X X X x X X X X x X X X X<br />X X X X X X X X X X X X<br />X X X X X X X X X X X X<br />X X X X X X X X X X X X<br />所以不要怕禁手。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-91482909527801629752016-02-24T11:25:45.604+08:002016-02-24T11:25:45.604+08:00從第一種有禁手的規則,並允許不連子,第十一條線,就要另闢戰場,應該可以很快找到規則性。
如果仍有禁...從第一種有禁手的規則,並允許不連子,第十一條線,就要另闢戰場,應該可以很快找到規則性。<br /><br />如果仍有禁手規定,並且要求必須連子,這又會是什麼情形?Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-62529078321724975112016-02-24T06:11:28.216+08:002016-02-24T06:11:28.216+08:00還有一點,在10連線時,最少用子是16子,但是此時的狀況是4x4的矩陣 https://www.de...還有一點,在10連線時,最少用子是16子,但是此時的狀況是4x4的矩陣 https://www.desmos.com/calculator/qotdusmep3<br />此時下每一步都是禁手。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-45864975933220223442016-02-24T05:42:38.855+08:002016-02-24T05:42:38.855+08:00我也有查覺到這一點,前面的結論有盡量避開這一部分。我也有查覺到這一點,前面的結論有盡量避開這一部分。.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-32557218132370344602016-02-23T07:57:18.421+08:002016-02-23T07:57:18.421+08:00謝謝老師提醒要點,對於五子以上連線,建議先用禁手方式處理,第二種處理方式視為同一條線,至於第三種多重...謝謝老師提醒要點,對於五子以上連線,建議先用禁手方式處理,第二種處理方式視為同一條線,至於第三種多重線重疊,個人不建議,因為它可以每加一子多一條線就沒什麼好玩。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-43977120213677198012016-02-23T07:23:42.201+08:002016-02-23T07:23:42.201+08:00當連線不斷增多時,禁手問題就突顯出來了。例如: XXXXX
這樣排列的五個棋子,應算1條連線,還是算...當連線不斷增多時,禁手問題就突顯出來了。例如: XXXXX<br />這樣排列的五個棋子,應算1條連線,還是算0條(因為超過4子連,視為禁手),抑或是算有三子重合的2條連線?如果是最後一種情況,那麼前面的結論要重新計算了。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-18814232515771720322016-02-22T18:44:43.243+08:002016-02-22T18:44:43.243+08:00關於數列尋找可參考舊文 http://4rdp.blogspot.tw/2013/07/oeis-a...關於數列尋找可參考舊文 http://4rdp.blogspot.tw/2013/07/oeis-a227392-1-2-2-3-5-6-10-6-9.htmlBridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-71573347158607048532016-02-22T13:07:28.497+08:002016-02-22T13:07:28.497+08:00是的,當斜率不限45度時,結論應該會不同是,不過在此仍限制45斜線,以簡化難度。
赤子西瓜的解答正確...是的,當斜率不限45度時,結論應該會不同是,不過在此仍限制45斜線,以簡化難度。<br />赤子西瓜的解答正確。接下來是進階題,當繼續擴展七連線以上,可否找到一個通解關係?我確定這是一個全新數列,有興趣的人努力找,西瓜它可以當你數學科展的好題材,加油。Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-86574301826463830872016-02-22T10:29:29.383+08:002016-02-22T10:29:29.383+08:00除了45度,如果還能接受其它斜率的直線,用子應該也會不同。除了45度,如果還能接受其它斜率的直線,用子應該也會不同。flyingdustshttps://www.blogger.com/profile/10543166743971149568noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-65878386397194088432016-02-21T22:54:10.012+08:002016-02-21T22:54:10.012+08:00四連線 https://www.desmos.com/calculator/po2zgcfof6 1...四連線 https://www.desmos.com/calculator/po2zgcfof6 11子<br />五連線 https://www.desmos.com/calculator/wykq4lci77 12子<br />六連線 https://www.desmos.com/calculator/cr81pmnfkq 13子.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-36873810794120723632016-02-18T23:24:02.265+08:002016-02-18T23:24:02.265+08:00三連線正解,但四、五、六連線再想想,你蠻厲害的,可以利用圖形計算機解題,讚!三連線正解,但四、五、六連線再想想,你蠻厲害的,可以利用圖形計算機解題,讚!Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-15623581891560535612016-02-18T22:27:07.461+08:002016-02-18T22:27:07.461+08:00https://www.desmos.com/calculator/6bwxga17xe
三線連成一...https://www.desmos.com/calculator/6bwxga17xe<br />三線連成一三角形,只要有三個點交會即可,原本三條線要用的12子,減去重複的3子,為9子。<br /><br />四連線:12子 https://www.desmos.com/calculator/ah5ej1jwjp<br />五連線:15子 https://www.desmos.com/calculator/e3cw4l1cgm<br />六連線:18子 https://www.desmos.com/calculator/f4gg1xfchm.https://www.blogger.com/profile/16677804023065232981noreply@blogger.comtag:blogger.com,1999:blog-3550204829234352390.post-15758940495031236872016-02-16T21:07:40.521+08:002016-02-16T21:07:40.521+08:00正解,請描述一下九子應該如何排列?
加分題,四子如果要四連線、五連線、六連線,各需要幾顆最少子?正解,請描述一下九子應該如何排列?<br /><br />加分題,四子如果要四連線、五連線、六連線,各需要幾顆最少子?Bridanhttps://www.blogger.com/profile/17055047757114667099noreply@blogger.com