Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:13:08.987Z Has data issue: false hasContentIssue false
  • English
  • Français

Mrs Perkins's quilt

Published online by Cambridge University Press:  24 October 2008

J. H. Conway
J. H. Conway
Affiliation:
Gonville and Caius College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we consider the problem of dividing a square of side N into squares of integral side. When we demand that these be unequal, the problem is soluble only for certain N, and has been treated in some detail by various authors (1,3,4,5). If we relax this condition, every side is permissible, for a square of side N may plainly be divided into N2 squares of side 1. It is the object of this paper to reduce this number: in fact we shall show that a square of side N is divisible into some number less than 6 ∛N + 1 squares of integral side.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 363 - 368
Copyright
Copyright © Cambridge Philosophical Society 1964

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

REFERENCES

(1) Brooks, R. L., Smith, C. A. B., Stone, A. H. and Tutte, W. T. Duke Math. J. 7 (1940), 312–340.CrossRefGoogle Scholar
(2) Dudeney, H. E. Amusements in mathematics (Dover; New York, 1959).Google Scholar
(3) Morón, Z. Przeglad Mat. Fiz. 3 (1925), 152–153.Google Scholar
(4) Sprague, R. Math. Z. 45 (1939), 607–608.CrossRefGoogle Scholar
(5) Willcocks, T. H. Canad. J. Math. 3 (1951), 304–308.CrossRefGoogle Scholar
(6) Moser, L. Proceedings of the 1963 Number Theory Conference (Boulder, Colorado), pp. 79–80 and 87–88.Google Scholar