Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-02T20:13:21.007Z Has data issue: false hasContentIssue false
  • English
  • Français

On Langford’s Problem (II)

Published online by Cambridge University Press:  03 November 2016

Roy O. Davies
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.