[問題] [跳出思路的陷阱]的陷阱
看板puzzle (益智遊戲 - 數獨,拼圖,推理,西洋棋)作者asdinap (asdinap)時間13年前 (2011/05/09 11:54)推噓50(50推 0噓 77→)留言127則, 12人參與討論串1/1
在[跳出思路的陷阱]這書上看到的題目 (就是下面這本書)
http://www.books.com.tw/exep/prod/booksfile.php?item=0010065033
其中有一題 毛毛蟲爬路 大概是說
一條繩100000cm 毛毛蟲1秒可以爬1cm 可是毛毛蟲每爬完一秒 繩就又多100000cm
問毛毛蟲有沒可能爬完這條繩
(繩的伸長應該在每秒爬完之後才伸長 若毛毛蟲某秒爬完 就不再伸長 算任務達成
上句原書沒寫 我個人依題意補充)
我個人心想: 每多過1秒 毛毛蟲就多99999cm要爬 越欠越多 鬼才有可能爬得完啦
不過如果爬不完 作者就不會寫這一題 於是作者竟然說
第1秒 毛毛蟲爬了 1cm = 爬完總任務的100000分之1 之後每秒多了100000cm
第2秒 毛毛蟲爬了 1cm = 爬完總任務的200000分之1
第3秒 毛毛蟲爬了 1cm = 爬完總任務的300000分之1
第4秒 毛毛蟲爬了 1cm = 爬完總任務的400000分之1 ..........餘此類推
所以 累積到第n秒 毛毛蟲爬了 總任務的
1/100000 * ( 1 + 1/2 + 1/3 + 1/4 + ....... + 1/n) = 1/100000*(調和級數)
只要 (調和級數) 到達100000 則 1/100000*(調和級數) = 1
也就是 毛毛蟲爬完總任務的1分之1 爬到終點了
然後調和級數是沒有上限的發散級數 因此總有一天會到達100000
所以雖然要很久很久 但是毛毛蟲爬得完
......最好爬得完啦! 請大家評評理投毛毛蟲爬不完一票吧~~~~~
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※ 編輯: asdinap 來自: 203.64.83.24 (05/09 11:54)
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