[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~~~~~
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 203.64.83.24
※ 編輯: asdinap 來自: 203.64.83.24 (05/09 11:54)
推
05/09 12:03, , 1F
05/09 12:03, 1F
推
05/09 12:04, , 2F
05/09 12:04, 2F
→
05/09 12:08, , 3F
05/09 12:08, 3F
→
05/09 12:09, , 4F
05/09 12:09, 4F
→
05/09 12:12, , 5F
05/09 12:12, 5F
推
05/09 12:36, , 6F
05/09 12:36, 6F
→
05/09 12:36, , 7F
05/09 12:36, 7F
推
05/09 12:59, , 8F
05/09 12:59, 8F
→
05/09 13:00, , 9F
05/09 13:00, 9F
推
05/09 13:04, , 10F
05/09 13:04, 10F
→
05/09 13:04, , 11F
05/09 13:04, 11F
→
05/09 13:04, , 12F
05/09 13:04, 12F
推
05/09 14:30, , 13F
05/09 14:30, 13F
推
05/09 14:34, , 14F
05/09 14:34, 14F
推
05/09 14:42, , 15F
05/09 14:42, 15F
推
05/09 16:04, , 16F
05/09 16:04, 16F
推
05/09 16:06, , 17F
05/09 16:06, 17F
→
05/09 16:16, , 18F
05/09 16:16, 18F
→
05/09 16:17, , 19F
05/09 16:17, 19F
→
05/09 16:19, , 20F
05/09 16:19, 20F
推
05/09 16:23, , 21F
05/09 16:23, 21F
推
05/09 16:26, , 22F
05/09 16:26, 22F
→
05/09 16:27, , 23F
05/09 16:27, 23F
→
05/09 16:28, , 24F
05/09 16:28, 24F
→
05/09 16:28, , 25F
05/09 16:28, 25F
推
05/09 16:30, , 26F
05/09 16:30, 26F
推
05/09 16:33, , 27F
05/09 16:33, 27F
推
05/09 16:34, , 28F
05/09 16:34, 28F
→
05/09 16:36, , 29F
05/09 16:36, 29F
推
05/09 16:37, , 30F
05/09 16:37, 30F
→
05/09 16:37, , 31F
05/09 16:37, 31F
推
05/09 16:41, , 32F
05/09 16:41, 32F
推
05/09 16:45, , 33F
05/09 16:45, 33F
→
05/09 16:45, , 34F
05/09 16:45, 34F
推
05/09 17:15, , 35F
05/09 17:15, 35F
→
05/09 17:15, , 36F
05/09 17:15, 36F
→
05/09 17:16, , 37F
05/09 17:16, 37F
→
05/09 17:17, , 38F
05/09 17:17, 38F
推
05/09 17:26, , 39F
05/09 17:26, 39F
還有 48 則推文
→
05/09 20:24, , 88F
05/09 20:24, 88F
→
05/09 20:25, , 89F
05/09 20:25, 89F
→
05/09 20:25, , 90F
05/09 20:25, 90F
推
05/09 20:27, , 91F
05/09 20:27, 91F
→
05/09 20:28, , 92F
05/09 20:28, 92F
→
05/09 20:32, , 93F
05/09 20:32, 93F
推
05/09 21:00, , 94F
05/09 21:00, 94F
→
05/09 21:02, , 95F
05/09 21:02, 95F
推
05/09 21:07, , 96F
05/09 21:07, 96F
推
05/09 21:10, , 97F
05/09 21:10, 97F
→
05/09 21:10, , 98F
05/09 21:10, 98F
→
05/09 21:11, , 99F
05/09 21:11, 99F
推
05/09 21:16, , 100F
05/09 21:16, 100F
→
05/09 21:19, , 101F
05/09 21:19, 101F
→
05/09 21:20, , 102F
05/09 21:20, 102F
推
05/09 21:21, , 103F
05/09 21:21, 103F
→
05/09 21:21, , 104F
05/09 21:21, 104F
→
05/09 21:23, , 105F
05/09 21:23, 105F
→
05/09 21:23, , 106F
05/09 21:23, 106F
推
05/09 21:26, , 107F
05/09 21:26, 107F
→
05/09 21:42, , 108F
05/09 21:42, 108F
推
05/09 21:43, , 109F
05/09 21:43, 109F
→
05/09 21:43, , 110F
05/09 21:43, 110F
→
05/09 21:43, , 111F
05/09 21:43, 111F
→
05/09 21:43, , 112F
05/09 21:43, 112F
→
05/09 21:44, , 113F
05/09 21:44, 113F
→
05/09 21:44, , 114F
05/09 21:44, 114F
→
05/09 21:45, , 115F
05/09 21:45, 115F
推
05/09 21:47, , 116F
05/09 21:47, 116F
→
05/09 21:48, , 117F
05/09 21:48, 117F
→
05/09 21:48, , 118F
05/09 21:48, 118F
→
05/09 21:49, , 119F
05/09 21:49, 119F
推
05/09 21:50, , 120F
05/09 21:50, 120F
推
05/09 21:52, , 121F
05/09 21:52, 121F
推
05/09 22:00, , 122F
05/09 22:00, 122F
→
05/09 22:01, , 123F
05/09 22:01, 123F
→
05/09 22:17, , 124F
05/09 22:17, 124F
推
05/09 23:18, , 125F
05/09 23:18, 125F
→
05/09 23:19, , 126F
05/09 23:19, 126F
→
05/09 23:21, , 127F
05/09 23:21, 127F
puzzle 近期熱門文章
PTT遊戲區 即時熱門文章
33
102