Please answer, it's important.
The six-spoked wheel shown has 19 circles placed
symmetrically on it, so that each spoke and section of the
rim contains three of them. The challenge is to find ways
of placing the numbers 1 to 19 in the circles so that the
total along each spoke and section of rim is the same.
One solution is partially completed to give you a flying
start.
Answers
Given : The six-spoked wheel shown has 19 circles placed
symmetrically on it, so that each spoke and section of the
rim contains three of them.
To Find : placing the numbers 1 to 19 in the circles so that the
total along each spoke and section of rim is the same.
Solution:
2 + 16 + 4 = 22
Hence each spoke and section of the rim sum = 22
2 + 12 + missing = 22 Hence 8
8 + missing + 4 = 22 => missing = 10
18 + 1 + 3 = 22 ( is only possibility )
so we get two case 1 can be on left or right of 18
Taking case 1 :
1 is on left of 18
hence 3 is on right of 18
15 will be between 3 and 4 to get 22
17 will be between 2 and 3
19 will be between 2 and 1
7 will be in side of 14
13 will be in between 7 and 2
9 will be in side of 6
11 will be in between 2 and 9
5 will be in between 9 and 8
Hence it becomes
1 18 3
14 19 17 15
7 13 2 16 4
6 11 12 10
9 5 8
Taking another case 3 is on left of 18
hence 1 is on right of 18
3 18 1
14 17 19 17
5 15 2 16 4
6 9 12 10
11 3 8
17 and 3 gets repeated 7 and 13 not used hence not a feasible solution
Only feasible solution is :
1 18 3
14 19 17 15
7 13 2 16 4
6 11 12 10
9 5 8
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