Langford series
by John from John D. Cook on (#748R3)
Notice anything special about the following sequence?
8 6 10 3 1 11 1 3 6 8 12 9 7 10 4 2 5 11 2 4 7 9 5 12
Each of the numbers 1 through 12 appear twice. Between the two 1s there is one number. Between the two 2s there are two numbers. Between the two 3s there are three numbers, etc.
Langford's problem of ordern is to arrange two copies of the integers 1 throughn so that there arek numbers between the twoks. This problem has a solution if and only ifn is congruent to 0 or 3 mod 4.
You can findmuch more on Langford's problem here.
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