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Binary Palindrome Square Magic (Posted on 2015-12-24) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts re(4): No Subject | Comment 6 of 11 |
(In reply to re(3): No Subject by Steve Herman)

I find your remarks inconsistent: you can't have your cake and eat it.

While it is true that classic definition of magic squares assumes  an array of distinct digits (default 1 to n^2)  there are numerous magic squares deviating from this default definition (use only primes, define sum other .5*n*(n+1), squares that remain magic rotated by 180 etc). Although some of these non-orthodox squares clearly imply (like in the binary palindrome case) use of repeated numbers, it would be nice to address the issue in the puzzle's text. I agree.

By the same token the standard notation of numbers is without leading zeroes: 2 in binary is 10, not 010 and 4 is written 100, not 00100. Unless specifically stated - "no leading zero presentation" is assumed.

The OEIS  listing has only one listing (not a single  even number), assuming standard notation:

A006995                    Binary palindromes: numbers whose binary expansion is palindromic

Even KS or SH, when told (without any disclaimer) to write 28 in binary, would without further questions  choose 11100, not 011100 and not 000011100.

Hope you understand my reservations.

Edited on December 25, 2015, 9:25 pm
  Posted by Ady TZIDON on 2015-12-25 21:13:57

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