Beauty of Magic Squares: 10,560-Multiple Order Bordered Striped Magic Squares of Order 144
This work presents 10,560 striped magic squares of order 144 (magic sum 1,493,064), constructed by the multiple order bordered method from width-2 magic rectangles. Order 144 is reached by three different routes. First, the main chain 12-24-40-60-84-112 (1440 squares of order 112) is continued by a ring of 32 striped magic squares of order 16; using 240 cores and twelve border variants gives 2880 squares. Second, the order-108 squares of Route A (108=6*18) receive a ring of 28 striped magic squares of order 18; twelve border variants give 2880 squares. Third, the order-108 squares of Route B, which already end with an order-18 ring, receive a second ring of order 18; ten border variants give 4800 squares --- the only squares in the series with two consecutive rings of the same block order. Together these give 2880+2880+4800=10,560 striped magic squares of order 144. Over the whole series (orders 24 to 144) a total of 17,578 striped magic squares are obtained. Excel files are attached with this work.
Authors
- Inder Jeet Taneja
Institutions
- Universidade Federal de Santa Catarina (BR)
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-11-01
- DOI
- https://doi.org/10.5281/zenodo.23852325
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- preprint