Talk:Sailors, coconuts and a monkey problem: Difference between revisions
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I do have to put in a ceiling - that gives me bound search time and protects me from "infinite loop" bugs while I'm playing with the code. But if a given value doesn't give me good results, it's trivial for me to multiply it by 10 and try again. I guess what I'm saying is that for this problem, this approach saved time for me. (But I guess you basically said this already, in your second paragraph.) --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 11:55, 3 May 2015 (UTC) |
I do have to put in a ceiling - that gives me bound search time and protects me from "infinite loop" bugs while I'm playing with the code. But if a given value doesn't give me good results, it's trivial for me to multiply it by 10 and try again. I guess what I'm saying is that for this problem, this approach saved time for me. (But I guess you basically said this already, in your second paragraph.) --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 11:55, 3 May 2015 (UTC) |
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== Analysis == |
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Let the solution be described by: |
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n6 g6 |
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n5 g5 |
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n4 g4 |
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n3 g3 |
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n2 g2 |
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n1 g1 |
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where n is the number of coconuts at each stage and g is the number of coconuts in each pile. |
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note that g1 is n1/5 and g2*4, which implies that n1 is divisible by 20. It is simple to calculate the entire table given n1. It is obvious that n1 is of the form X + (4*5)*2*(2*)*(2*2)*(2*2*2*2) or 5120. X is divisible by 20 and less than 5120. Which implies that J's maximum value is justified if over generous. By examination X must be a member of the series 20 + 40*z. Let us look at that: |
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20 26 33.5 42.875 |
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60 76 96 121 |
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100 126 158.5 199.125 |
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140 176 221 277.25 |
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180 226 283.5 355.375 |
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220 276 346 433.5 |
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260 326 408.5 511.625 |
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300 376 471 589.75 |
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340 426 533.5 667.875 |
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380 476 596 746 |
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420 526 658.5 824.125 |
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460 576 721 902.25 |
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By examining the 4th column we can see that when the step is 320 ((4*5)*2*(2*)*(2*2) X is 60. So X must be a member of the series 60 + 320*z. Let us look at that: |
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60 76 96 121 152.25 191.3125 |
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380 476 596 746 933.5 1167.875 |
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700 876 1096 1371 1714.75 2144.4375 |
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1020 1276 1596 1996 2496 3121 |
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1340 1676 2096 2621 3277.25 4097.5625 |
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1660 2076 2596 3246 4058.5 5074.125 |
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1980 2476 3096 3871 4839.75 6050.6875 |
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2300 2876 3596 4496 5621 7027.25 |
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2620 3276 4096 5121 6402.25 8003.8125 |
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2940 3676 4596 5746 7183.5 8980.375 |
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3260 4076 5096 6371 7964.75 9956.9375 |
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3580 4476 5596 6996 8746 10933.5 |
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3900 4876 6096 7621 9527.25 11910.0625 |
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4220 5276 6596 8246 10308.5 12886.625 |
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4540 5676 7096 8871 11089.75 13863.1875 |
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4860 6076 7596 9496 11871 14839.75 |
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5180 6476 8096 10121 12652.25 15816.3125 |
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5500 6876 8596 10746 13433.5 16792.875 |
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5820 7276 9096 11371 14214.75 17769.4375 |
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6140 7676 9596 11996 14996 18746 |
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6460 8076 10096 12621 15777.25 19722.5625 |
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6780 8476 10596 13246 16558.5 20699.125 |
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7100 8876 11096 13871 17339.75 21675.6875 |
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7420 9276 11596 14496 18121 22652.25 |
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7740 9676 12096 15121 18902.25 23628.8125 |
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8060 10076 12596 15746 19683.5 24605.375 |
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8380 10476 13096 16371 20464.75 25581.9375 |
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8700 10876 13596 16996 21246 26558.5 |
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9020 11276 14096 17621 22027.25 27535.0625 |
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9340 11676 14596 18246 22808.5 28511.625 |
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9660 12076 15096 18871 23589.75 29488.1875 |
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9980 12476 15596 19496 24371 30464.75 |
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10300 12876 16096 20121 25152.25 31441.3125 |
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10620 13276 16596 20746 25933.5 32417.875 |
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10940 13676 17096 21371 26714.75 33394.4375 |
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11260 14076 17596 21996 27496 34371 |
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11580 14476 18096 22621 28277.25 35347.5625 |
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11900 14876 18596 23246 29058.5 36324.125 |
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12220 15276 19096 23871 29839.75 37300.6875 |
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12540 15676 19596 24496 30621 38277.25 |
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12860 16076 20096 25121 31402.25 39253.8125 |
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13180 16476 20596 25746 32183.5 40230.375 |
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13500 16876 21096 26371 32964.75 41206.9375 |
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13820 17276 21596 26996 33746 42183.5 |
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14140 17676 22096 27621 34527.25 43160.0625 |
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14460 18076 22596 28246 35308.5 44136.625 |
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14780 18476 23096 28871 36089.75 45113.1875 |
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15100 18876 23596 29496 36871 46089.75 |
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15420 19276 24096 30121 37652.25 47066.3125 |
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Examination of the final column we see that for the step of 5120 "(4*5)*2*(2*)*(2*2)*(2*2*2*2)" X is 1020. |
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--[[User:Nigel Galloway|Nigel Galloway]] ([[User talk:Nigel Galloway|talk]]) 09:44, 5 May 2015 (UTC) |