Published June 28, 2020 | Version v1
Preprint Open

Universal Magic Squares of Type 4k, 6k and 12k Using the Digits 2 and 5

  • 1. Formarly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil

Description

This work brings magic squares of multiples of 4k, 6k and 12k using the digits 2 and 5. Each magic square contains 12-digits in each cell. Just with two digits, one can have exactly 1024 different possibilities of 12-digits combinations from two digits. In case of 4k, we have written magic squares of orders: 4, 8,...., 60 and 64. In case 6k, we have written magic square of orders: 6, 12, ..., 54 and 60. In case of 12k, we have written magic square of orders: 6, 12, 24, 36, 48 and 60. All the blocks of magic squares of orders 4, 6 and 12 are with equal sums in each case. Similar works for the digits 1 and 8, and the digits 6 and 9 are done in another papers. The work on multiples of 3, 5, 7, etc. shall be done elsewhere. Later, the work shall be extended up to magic squares of order 128 having 14-digits in each cell just with two digits: {1,8}, {2,5} and {6,9}. In the first two cases the work is always upside-down and mirror looking, while in the third case for the digits 6 and 9, the work is only upside-down. When the magic squares are upside-down and mirror looking, we call them as universal magic squares. In order to have universal magic squares, the digits 2 and 5 are written in digital form. The whole work is without use of any programming language. It is just based on the number's combinations.

Files

Universal-25.pdf

Files (8.9 MB)

Name Size Download all
md5:081c78284d4d885c115cb319bdebd75d
8.9 MB Preview Download