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On Langford’s Problem (II)

Published online by Cambridge University Press:  03 November 2016

Roy O. Davies
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Extract

The problem is to arrange the numbers 1, 1, 2, 2, …, n, n in a sequence (without gaps) in such a way that for r = 1, 2, …, n the two r’s are separated by exactly r places; for example

41312432.

Priday has shown in the preceding paper that for every n there exists either such a perfect sequence (as he calls it) or else a hooked sequence, with a gap one place from one end, for example

345131425*2.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 43 , Issue 346 , December 1959 , pp. 253 - 255
Copyright
Copyright © Mathematical Association 1959

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References

page note 253 ‡ Th. Skolem. On certain distributions of integers in pairs with given differences. Math. Scand. 5 (1957), 57–68.

page 255 of note † Th. Skolem. Some remarks on the triple systems of Steiner. Math. Scand. 6 (1958), 273–280, esp. p. 274.