FIRST METHOD (Given by Charlie):
Charlie's methodologies culminating in a comprehensive soluion to the problem under reference are given in location1; location2; and location3.
SECOND METHOD:
One of the arrangements is given by :
1, 33, 17, 9, 41, 25, 5 ,37, 21, 13, 45, 29, 3, 35, 19, 11, 43, 27, 7, 39, 23, 15, 47, 31, 2, 34,18, 10, 42, 26, 6, 38, 22, 14, 46, 30, 4, 36, 20, 12, 44, 28, 8, 40, 24, 16, 32.
This is obtained in the following manner.
First, we arrange the disks from 1 to 47 left to right. This gives us one "group" of disks.
We now repeat the following for every group:
1. Pulling the first disk to the left to start a new group.
2. Adding every other disk to the new group in order.
3. We now have twice as many groups, each half the size of the first. The process is repeated until every group is of size 1 or 2.
Consequently, we obtain:
First group: 1-47
Second groups: (1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47) ( 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46)
Third groups: (1 5 9 13 17 21 25 29 33 37 41 45) (3 7 11 15 19 23 27 31 35 39 43 47) (2 6 10 14 18 22 26 30 34 38 42 46) (4 8 12 16 20 24 28 32 36 40 44)
Fourth groups: (1 9 17 25 33 41)(5 13 21 29 37 45) (3 11 19 27 35 43) (7 15 23 31 39 47) (2 10 18 26 34 42) (6 14 22 30 38 46) (4 12 20 28 36 44) ( 8 16 24 32 40)
Fifth Groups: ( 1 17 33) ( 9 25 41)( 5 21 37)(13 29 45) (3 19 35) (11 27 43) (7 23 39)(15 31 47) (2 18 34) (10 26 42)(6 22 38)(14 30 46) (4 20 36)(12 28 44)(8 24 40)(16 32)
Sixth And Final Groups: (1 33)(17)(9 41)(25)(5 37)(21)(13 45)(29)(3 35)(19)(11 43)(27)(7 39)(23)(15 47)(31)(2 34)(18)(10 42)(26)(6 38)(22)(14 46)(30)(4 36)(20)(12 44)(28)(8 40)(24)(16 32)
Consequently, the required arrangement is:
1, 33, 17, 9, 41, 25, 5 ,37, 21, 13, 45, 29, 3, 35, 19, 11, 43, 27, 7, 39, 23, 15, 47, 31, 2, 34,18, 10, 42, 26, 6, 38, 22, 14, 46, 30, 4, 36, 20, 12, 44, 28, 8, 40, 24, 16, 32.
N.B.: Within each group it does not matter whether the odd or even ones go left or right as has been rightly pointed out by Charlie in this location.
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