Beauty of Magic Squares: Multiple Order Bordered Striped Magic Squares of Orders 24, 40, 60 and 84

A striped magic square is a magic square built entirely from magic rectangles of equal width 2. This work constructs very large striped magic squares by the multiple order bordered method: a striped magic square of order n divisible by an even number m is surrounded by a ring of width m made of striped magic squares of order m (with different magic sums, giving a new striped magic square of order n+2m. Starting from a striped magic square of order 12 (nine equal-sum striped squares of order 4), rings of orders 6, 8, 10 and 12 give striped magic squares of orders 24, 40, 60 and 84, with magic sums 6,924, 32,020, 108,030 and 296,394. Combining every core with every border variant gives 2, 8, 48 and 240 squares respectively, a total of 298 striped magic squares. The orders follow the beautiful pattern N_k=2k(k+1)=4T_k (four times a triangular number), so the chain continues naturally to orders 112 and 144, studied in the later parts of this series. The excel file of complete work is attached.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-01
DOI
https://doi.org/10.5281/zenodo.23852133
Primary Topic
Advanced Combinatorial Mathematics
Type
preprint
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preprint

Beauty of Magic Squares: Multiple Order Bordered Striped Magic Squares of Orders 24, 40, 60 and 84

Inder Jeet Taneja
4 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Combinatorial Mathematics
preprint

Beauty of Magic Squares: Multiple Order Bordered Striped Magic Squares of Orders 24, 40, 60 and 84

Inder Jeet Taneja
preprint en

Abstract

A striped magic square is a magic square built entirely from magic rectangles of equal width 2. This work constructs very large striped magic squares by the multiple order bordered method: a striped magic square of order n divisible by an even number m is surrounded by a ring of width m made of striped magic squares of order m (with different magic sums, giving a new striped magic square of order n+2m. Starting from a striped magic square of order 12 (nine equal-sum striped squares of order 4), rings of orders 6, 8, 10 and 12 give striped magic squares of orders 24, 40, 60 and 84, with magic sums 6,924, 32,020, 108,030 and 296,394. Combining every core with every border variant gives 2, 8, 48 and 240 squares respectively, a total of 298 striped magic squares. The orders follow the beautiful pattern N_k=2k(k+1)=4T_k (four times a triangular number), so the chain continues naturally to orders 112 and 144, studied in the later parts of this series. The excel file of complete work is attached.

Zenodo (CERN European Organization for Nuclear Research)
Universidade Federal de Santa Catarina (BR)
Advanced Combinatorial Mathematics
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Beauty of Magic Squares: Multiple Order Bordered Striped Magic Squares of Orders 24, 40, 60 and 84 — Inder Jeet Taneja · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS