On The Ramsgate Sands
(
MISCELLANEOUS PUZZLES)
Thirteen youngsters were seen dancing in a ring on the Ramsgate sands. Apparently they were playing "Round the Mulberry Bush." The puzzle is this. How many rings may they form without any child ever taking twice the hand of any other child—right hand or left? That is, no child may ever have a second time the same neighbour.
Answer:
Just six different rings may be formed without breaking the conditions. Here is one way of effecting the arrangements.
A |
B |
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D |
E |
F |
G |
H |
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J |
K |
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M |
A |
C |
E |
G |
I |
K |
M |
B |
D |
F |
H |
J |
L |
A |
D |
G |
J |
M |
C |
F |
I |
L |
B |
E |
H |
K |
A |
E |
I |
M |
D |
H |
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C |
G |
K |
B |
F |
J |
A |
F |
K |
C |
H |
M |
E |
J |
B |
G |
L |
D |
I |
A |
G |
M |
F |
L |
E |
K |
D |
J |
C |
I |
B |
H |
Join the ends and you have the six rings.
Lucas devised a simple mechanical method for obtaining the n rings that may be formed under the conditions by 2n+1 children.
