Most-perfect magic square

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Most-perfect magic square" – news · newspapers · books · scholar · JSTOR (July 2021) (Learn how and when to remove this message)

A most-perfect magic square of order n is a magic square containing the numbers 1 to n² with two additional properties:

1. Each 2 × 2 subsquare sums to 2s, where s = n² + 1.
2. All pairs of integers distant n/2 along a (major) diagonal sum to s.

A suggestive form for a 4 × 4 most-perfect magic square with magic constant = 34, is:

with the additional constraint that no cell may equal any other to get consecutive numbers from 1 to 16.

There are 384 such combinations.