Find a 4x4 magic square with magic constant being 188 (base ten) and each of whose 16 entries is a non leading zeroes positive binary palindrome.
*** Disregard rotations and reflections.
A traditional normal magic square is a matrix of numbers of 1 to n^2, with each number occuring once, with each row, column, and main diagonal having the same sum.
A Sagrada Família magic square is a magic square where the numbers are not all unique and are not all necessarily consecutive to that of another number in the set of numbers that comprise the magic square. It is possible that this puzzle's Binary Palindrome Magic Square is a subset of the Sagrada Familia magic squares. Each row, column, and main diagonal should still have the same sum, yet the numbers do not have to be "consecutive" palindromic numbers, nor do they need all be unique.
There are variations to magic squares, but generally the constraint is that each row, column and main diagonal sum to the same total, and -- outside the Sagrada Familia magic squares -- each number is unique, such as in the multiplicative magic squares and magic squares of primes. Given the constraint of each number being unique, a magic square of binary palindromes might not be possible for the given magic constant.
A good question is then, does there exist a Binary Palindrome magic square as opposed to a Binary Palindrome Sagrada Familia magic square? And, if one does exist, does it exist for the magic constant 188?
Posted by Dej Mar
on 2015-12-26 04:31:42