Talk:Sailors, coconuts and a monkey problem: Difference between revisions
Content added Content deleted
No edit summary |
|||
| Line 10: | Line 10: | ||
Let the solution be described by: |
Let the solution be described by: |
||
<pre> |
|||
n6 g6 |
n6 g6 |
||
n5 g5 |
n5 g5 |
||
| Line 17: | Line 17: | ||
n2 g2 |
n2 g2 |
||
n1 g1 |
n1 g1 |
||
</pre> |
|||
where n is the number of coconuts at each stage and g is the number of coconuts in each pile. |
where n is the number of coconuts at each stage and g is the number of coconuts in each pile. |
||
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: |
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: |
||
<pre> |
|||
20 26 33.5 42.875 |
20 26 33.5 42.875 |
||
60 76 96 121 |
60 76 96 121 |
||
| Line 34: | Line 34: | ||
420 526 658.5 824.125 |
420 526 658.5 824.125 |
||
460 576 721 902.25 |
460 576 721 902.25 |
||
</pre> |
|||
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: |
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: |
||
<pre> |
|||
60 76 96 121 152.25 191.3125 |
60 76 96 121 152.25 191.3125 |
||
380 476 596 746 933.5 1167.875 |
380 476 596 746 933.5 1167.875 |
||
| Line 86: | Line 86: | ||
15100 18876 23596 29496 36871 46089.75 |
15100 18876 23596 29496 36871 46089.75 |
||
15420 19276 24096 30121 37652.25 47066.3125 |
15420 19276 24096 30121 37652.25 47066.3125 |
||
</pre> |
|||
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. |
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. |
||