Books about
Magic Squares
at Amazon.Canada


Amazing Math Whiz
products available:

Buttons, Magnets,
t-shirts, Tote bags,
Teddy bears, & more

Books about Magic Squares at Amazon.com

Be sure to visit the
Magic Squares Main Menu
for other topics including Irregular Squares, Algebraic Squares and more.

Other Magic Square Sizes: 3 * 5 * 7 * 9 * 11 * 13 * 15 * 17 * 19 *
21 * 23 * 25 * 27 * 29 * 31 * 33 * 35 * 37 * 39 * 41 * 43 * 45 * 47 * 49 * 51 * 53 * 55 * 57 * 59 *
61 * 63 * 65 * 67 * 69 * 71 * 73 * 75 * 77 * 79 * 81 * 83 * 85 * 87 * 89 * 91 * 93 * 95 * 97 * 99 *

A 59x59 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (102719)

A Magic Square is a square of numbers in which every row, every column, and both diagonals add up to the same number. This number is often called the magic sum. The 59 by 59 magic square shown below has a magic sum equal to 102719.

Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers. To the best of my knowledge, the middle number in the sequence must be in the center square, and the magic sum will be equal to this middle number times the number of rows in the square. (In the case of 3x3 squares, I have proved that the middle number MUST be equal to one-third of the sum. See proof here.)

All odd-size Magic Squares can be made with the method shown below, which can be summarized as "start in the middle of the top and keep moving up and to the right except when you get blocked, in which case drop down and continue." The more detailed directions about creating these squares can be found further below. There are other methods for creating magic squares, but this is the easiest to learn. (There are basically only two methods of creating a 3x3 square but the larger squares have a large number of irregular variants, and probably other regular methods.)

Read more about Magic Squares

If you'd like to read more about magic squares, click one of these links to look for books about Magic Squares at Amazon.com, at Amazon.canada, and at Amazon.co.UK.

A 59-by-59 Magic Square

(Magic Sum = 102719)

Books about
Magic Squares
at Amazon.co.UK


Support Our Site
by purchasing our
Amazing Math Whiz
products

and other
Amazing Messages

1772 1833 1894 1955 2016 2077 2138 2199 2260 2321 2382 2443 2504 2565 2626 2687 2748 2809 2870 2931 2992 3053 3114 3175 3236 3297 3358 3419 3480 1 62 123 184 245 306 367 428 489 550 611 672 733 794 855 916 977 1038 1099 1160 1221 1282 1343 1404 1465 1526 1587 1648 1709 1770
1832 1893 1954 2015 2076 2137 2198 2259 2320 2381 2442 2503 2564 2625 2686 2747 2808 2869 2930 2991 3052 3113 3174 3235 3296 3357 3418 3479 59 61 122 183 244 305 366 427 488 549 610 671 732 793 854 915 976 1037 1098 1159 1220 1281 1342 1403 1464 1525 1586 1647 1708 1769 1771
1892 1953 2014 2075 2136 2197 2258 2319 2380 2441 2502 2563 2624 2685 2746 2807 2868 2929 2990 3051 3112 3173 3234 3295 3356 3417 3478 58 60 121 182 243 304 365 426 487 548 609 670 731 792 853 914 975 1036 1097 1158 1219 1280 1341 1402 1463 1524 1585 1646 1707 1768 1829 1831
1952 2013 2074 2135 2196 2257 2318 2379 2440 2501 2562 2623 2684 2745 2806 2867 2928 2989 3050 3111 3172 3233 3294 3355 3416 3477 57 118 120 181 242 303 364 425 486 547 608 669 730 791 852 913 974 1035 1096 1157 1218 1279 1340 1401 1462 1523 1584 1645 1706 1767 1828 1830 1891
2012 2073 2134 2195 2256 2317 2378 2439 2500 2561 2622 2683 2744 2805 2866 2927 2988 3049 3110 3171 3232 3293 3354 3415 3476 56 117 119 180 241 302 363 424 485 546 607 668 729 790 851 912 973 1034 1095 1156 1217 1278 1339 1400 1461 1522 1583 1644 1705 1766 1827 1888 1890 1951
2072 2133 2194 2255 2316 2377 2438 2499 2560 2621 2682 2743 2804 2865 2926 2987 3048 3109 3170 3231 3292 3353 3414 3475 55 116 177 179 240 301 362 423 484 545 606 667 728 789 850 911 972 1033 1094 1155 1216 1277 1338 1399 1460 1521 1582 1643 1704 1765 1826 1887 1889 1950 2011
2132 2193 2254 2315 2376 2437 2498 2559 2620 2681 2742 2803 2864 2925 2986 3047 3108 3169 3230 3291 3352 3413 3474 54 115 176 178 239 300 361 422 483 544 605 666 727 788 849 910 971 1032 1093 1154 1215 1276 1337 1398 1459 1520 1581 1642 1703 1764 1825 1886 1947 1949 2010 2071
2192 2253 2314 2375 2436 2497 2558 2619 2680 2741 2802 2863 2924 2985 3046 3107 3168 3229 3290 3351 3412 3473 53 114 175 236 238 299 360 421 482 543 604 665 726 787 848 909 970 1031 1092 1153 1214 1275 1336 1397 1458 1519 1580 1641 1702 1763 1824 1885 1946 1948 2009 2070 2131
2252 2313 2374 2435 2496 2557 2618 2679 2740 2801 2862 2923 2984 3045 3106 3167 3228 3289 3350 3411 3472 52 113 174 235 237 298 359 420 481 542 603 664 725 786 847 908 969 1030 1091 1152 1213 1274 1335 1396 1457 1518 1579 1640 1701 1762 1823 1884 1945 2006 2008 2069 2130 2191
2312 2373 2434 2495 2556 2617 2678 2739 2800 2861 2922 2983 3044 3105 3166 3227 3288 3349 3410 3471 51 112 173 234 295 297 358 419 480 541 602 663 724 785 846 907 968 1029 1090 1151 1212 1273 1334 1395 1456 1517 1578 1639 1700 1761 1822 1883 1944 2005 2007 2068 2129 2190 2251
2372 2433 2494 2555 2616 2677 2738 2799 2860 2921 2982 3043 3104 3165 3226 3287 3348 3409 3470 50 111 172 233 294 296 357 418 479 540 601 662 723 784 845 906 967 1028 1089 1150 1211 1272 1333 1394 1455 1516 1577 1638 1699 1760 1821 1882 1943 2004 2065 2067 2128 2189 2250 2311
2432 2493 2554 2615 2676 2737 2798 2859 2920 2981 3042 3103 3164 3225 3286 3347 3408 3469 49 110 171 232 293 354 356 417 478 539 600 661 722 783 844 905 966 1027 1088 1149 1210 1271 1332 1393 1454 1515 1576 1637 1698 1759 1820 1881 1942 2003 2064 2066 2127 2188 2249 2310 2371
2492 2553 2614 2675 2736 2797 2858 2919 2980 3041 3102 3163 3224 3285 3346 3407 3468 48 109 170 231 292 353 355 416 477 538 599 660 721 782 843 904 965 1026 1087 1148 1209 1270 1331 1392 1453 1514 1575 1636 1697 1758 1819 1880 1941 2002 2063 2124 2126 2187 2248 2309 2370 2431
2552 2613 2674 2735 2796 2857 2918 2979 3040 3101 3162 3223 3284 3345 3406 3467 47 108 169 230 291 352 413 415 476 537 598 659 720 781 842 903 964 1025 1086 1147 1208 1269 1330 1391 1452 1513 1574 1635 1696 1757 1818 1879 1940 2001 2062 2123 2125 2186 2247 2308 2369 2430 2491
2612 2673 2734 2795 2856 2917 2978 3039 3100 3161 3222 3283 3344 3405 3466 46 107 168 229 290 351 412 414 475 536 597 658 719 780 841 902 963 1024 1085 1146 1207 1268 1329 1390 1451 1512 1573 1634 1695 1756 1817 1878 1939 2000 2061 2122 2183 2185 2246 2307 2368 2429 2490 2551
2672 2733 2794 2855 2916 2977 3038 3099 3160 3221 3282 3343 3404 3465 45 106 167 228 289 350 411 472 474 535 596 657 718 779 840 901 962 1023 1084 1145 1206 1267 1328 1389 1450 1511 1572 1633 1694 1755 1816 1877 1938 1999 2060 2121 2182 2184 2245 2306 2367 2428 2489 2550 2611
2732 2793 2854 2915 2976 3037 3098 3159 3220 3281 3342 3403 3464 44 105 166 227 288 349 410 471 473 534 595 656 717 778 839 900 961 1022 1083 1144 1205 1266 1327 1388 1449 1510 1571 1632 1693 1754 1815 1876 1937 1998 2059 2120 2181 2242 2244 2305 2366 2427 2488 2549 2610 2671
2792 2853 2914 2975 3036 3097 3158 3219 3280 3341 3402 3463 43 104 165 226 287 348 409 470 531 533 594 655 716 777 838 899 960 1021 1082 1143 1204 1265 1326 1387 1448 1509 1570 1631 1692 1753 1814 1875 1936 1997 2058 2119 2180 2241 2243 2304 2365 2426 2487 2548 2609 2670 2731
2852 2913 2974 3035 3096 3157 3218 3279 3340 3401 3462 42 103 164 225 286 347 408 469 530 532 593 654 715 776 837 898 959 1020 1081 1142 1203 1264 1325 1386 1447 1508 1569 1630 1691 1752 1813 1874 1935 1996 2057 2118 2179 2240 2301 2303 2364 2425 2486 2547 2608 2669 2730 2791
2912 2973 3034 3095 3156 3217 3278 3339 3400 3461 41 102 163 224 285 346 407 468 529 590 592 653 714 775 836 897 958 1019 1080 1141 1202 1263 1324 1385 1446 1507 1568 1629 1690 1751 1812 1873 1934 1995 2056 2117 2178 2239 2300 2302 2363 2424 2485 2546 2607 2668 2729 2790 2851
2972 3033 3094 3155 3216 3277 3338 3399 3460 40 101 162 223 284 345 406 467 528 589 591 652 713 774 835 896 957 1018 1079 1140 1201 1262 1323 1384 1445 1506 1567 1628 1689 1750 1811 1872 1933 1994 2055 2116 2177 2238 2299 2360 2362 2423 2484 2545 2606 2667 2728 2789 2850 2911
3032 3093 3154 3215 3276 3337 3398 3459 39 100 161 222 283 344 405 466 527 588 649 651 712 773 834 895 956 1017 1078 1139 1200 1261 1322 1383 1444 1505 1566 1627 1688 1749 1810 1871 1932 1993 2054 2115 2176 2237 2298 2359 2361 2422 2483 2544 2605 2666 2727 2788 2849 2910 2971
3092 3153 3214 3275 3336 3397 3458 38 99 160 221 282 343 404 465 526 587 648 650 711 772 833 894 955 1016 1077 1138 1199 1260 1321 1382 1443 1504 1565 1626 1687 1748 1809 1870 1931 1992 2053 2114 2175 2236 2297 2358 2419 2421 2482 2543 2604 2665 2726 2787 2848 2909 2970 3031
3152 3213 3274 3335 3396 3457 37 98 159 220 281 342 403 464 525 586 647 708 710 771 832 893 954 1015 1076 1137 1198 1259 1320 1381 1442 1503 1564 1625 1686 1747 1808 1869 1930 1991 2052 2113 2174 2235 2296 2357 2418 2420 2481 2542 2603 2664 2725 2786 2847 2908 2969 3030 3091
3212 3273 3334 3395 3456 36 97 158 219 280 341 402 463 524 585 646 707 709 770 831 892 953 1014 1075 1136 1197 1258 1319 1380 1441 1502 1563 1624 1685 1746 1807 1868 1929 1990 2051 2112 2173 2234 2295 2356 2417 2478 2480 2541 2602 2663 2724 2785 2846 2907 2968 3029 3090 3151
3272 3333 3394 3455 35 96 157 218 279 340 401 462 523 584 645 706 767 769 830 891 952 1013 1074 1135 1196 1257 1318 1379 1440 1501 1562 1623 1684 1745 1806 1867 1928 1989 2050 2111 2172 2233 2294 2355 2416 2477 2479 2540 2601 2662 2723 2784 2845 2906 2967 3028 3089 3150 3211
3332 3393 3454 34 95 156 217 278 339 400 461 522 583 644 705 766 768 829 890 951 1012 1073 1134 1195 1256 1317 1378 1439 1500 1561 1622 1683 1744 1805 1866 1927 1988 2049 2110 2171 2232 2293 2354 2415 2476 2537 2539 2600 2661 2722 2783 2844 2905 2966 3027 3088 3149 3210 3271
3392 3453 33 94 155 216 277 338 399 460 521 582 643 704 765 826 828 889 950 1011 1072 1133 1194 1255 1316 1377 1438 1499 1560 1621 1682 1743 1804 1865 1926 1987 2048 2109 2170 2231 2292 2353 2414 2475 2536 2538 2599 2660 2721 2782 2843 2904 2965 3026 3087 3148 3209 3270 3331
3452 32 93 154 215 276 337 398 459 520 581 642 703 764 825 827 888 949 1010 1071 1132 1193 1254 1315 1376 1437 1498 1559 1620 1681 1742 1803 1864 1925 1986 2047 2108 2169 2230 2291 2352 2413 2474 2535 2596 2598 2659 2720 2781 2842 2903 2964 3025 3086 3147 3208 3269 3330 3391
31 92 153 214 275 336 397 458 519 580 641 702 763 824 885 887 948 1009 1070 1131 1192 1253 1314 1375 1436 1497 1558 1619 1680 1741 1802 1863 1924 1985 2046 2107 2168 2229 2290 2351 2412 2473 2534 2595 2597 2658 2719 2780 2841 2902 2963 3024 3085 3146 3207 3268 3329 3390 3451
91 152 213 274 335 396 457 518 579 640 701 762 823 884 886 947 1008 1069 1130 1191 1252 1313 1374 1435 1496 1557 1618 1679 1740 1801 1862 1923 1984 2045 2106 2167 2228 2289 2350 2411 2472 2533 2594 2655 2657 2718 2779 2840 2901 2962 3023 3084 3145 3206 3267 3328 3389 3450 30
151 212 273 334 395 456 517 578 639 700 761 822 883 944 946 1007 1068 1129 1190 1251 1312 1373 1434 1495 1556 1617 1678 1739 1800 1861 1922 1983 2044 2105 2166 2227 2288 2349 2410 2471 2532 2593 2654 2656 2717 2778 2839 2900 2961 3022 3083 3144 3205 3266 3327 3388 3449 29 90
211 272 333 394 455 516 577 638 699 760 821 882 943 945 1006 1067 1128 1189 1250 1311 1372 1433 1494 1555 1616 1677 1738 1799 1860 1921 1982 2043 2104 2165 2226 2287 2348 2409 2470 2531 2592 2653 2714 2716 2777 2838 2899 2960 3021 3082 3143 3204 3265 3326 3387 3448 28 89 150
271 332 393 454 515 576 637 698 759 820 881 942 1003 1005 1066 1127 1188 1249 1310 1371 1432 1493 1554 1615 1676 1737 1798 1859 1920 1981 2042 2103 2164 2225 2286 2347 2408 2469 2530 2591 2652 2713 2715 2776 2837 2898 2959 3020 3081 3142 3203 3264 3325 3386 3447 27 88 149 210
331 392 453 514 575 636 697 758 819 880 941 1002 1004 1065 1126 1187 1248 1309 1370 1431 1492 1553 1614 1675 1736 1797 1858 1919 1980 2041 2102 2163 2224 2285 2346 2407 2468 2529 2590 2651 2712 2773 2775 2836 2897 2958 3019 3080 3141 3202 3263 3324 3385 3446 26 87 148 209 270
391 452 513 574 635 696 757 818 879 940 1001 1062 1064 1125 1186 1247 1308 1369 1430 1491 1552 1613 1674 1735 1796 1857 1918 1979 2040 2101 2162 2223 2284 2345 2406 2467 2528 2589 2650 2711 2772 2774 2835 2896 2957 3018 3079 3140 3201 3262 3323 3384 3445 25 86 147 208 269 330
451 512 573 634 695 756 817 878 939 1000 1061 1063 1124 1185 1246 1307 1368 1429 1490 1551 1612 1673 1734 1795 1856 1917 1978 2039 2100 2161 2222 2283 2344 2405 2466 2527 2588 2649 2710 2771 2832 2834 2895 2956 3017 3078 3139 3200 3261 3322 3383 3444 24 85 146 207 268 329 390
511 572 633 694 755 816 877 938 999 1060 1121 1123 1184 1245 1306 1367 1428 1489 1550 1611 1672 1733 1794 1855 1916 1977 2038 2099 2160 2221 2282 2343 2404 2465 2526 2587 2648 2709 2770 2831 2833 2894 2955 3016 3077 3138 3199 3260 3321 3382 3443 23 84 145 206 267 328 389 450
571 632 693 754 815 876 937 998 1059 1120 1122 1183 1244 1305 1366 1427 1488 1549 1610 1671 1732 1793 1854 1915 1976 2037 2098 2159 2220 2281 2342 2403 2464 2525 2586 2647 2708 2769 2830 2891 2893 2954 3015 3076 3137 3198 3259 3320 3381 3442 22 83 144 205 266 327 388 449 510
631 692 753 814 875 936 997 1058 1119 1180 1182 1243 1304 1365 1426 1487 1548 1609 1670 1731 1792 1853 1914 1975 2036 2097 2158 2219 2280 2341 2402 2463 2524 2585 2646 2707 2768 2829 2890 2892 2953 3014 3075 3136 3197 3258 3319 3380 3441 21 82 143 204 265 326 387 448 509 570
691 752 813 874 935 996 1057 1118 1179 1181 1242 1303 1364 1425 1486 1547 1608 1669 1730 1791 1852 1913 1974 2035 2096 2157 2218 2279 2340 2401 2462 2523 2584 2645 2706 2767 2828 2889 2950 2952 3013 3074 3135 3196 3257 3318 3379 3440 20 81 142 203 264 325 386 447 508 569 630
751 812 873 934 995 1056 1117 1178 1239 1241 1302 1363 1424 1485 1546 1607 1668 1729 1790 1851 1912 1973 2034 2095 2156 2217 2278 2339 2400 2461 2522 2583 2644 2705 2766 2827 2888 2949 2951 3012 3073 3134 3195 3256 3317 3378 3439 19 80 141 202 263 324 385 446 507 568 629 690
811 872 933 994 1055 1116 1177 1238 1240 1301 1362 1423 1484 1545 1606 1667 1728 1789 1850 1911 1972 2033 2094 2155 2216 2277 2338 2399 2460 2521 2582 2643 2704 2765 2826 2887 2948 3009 3011 3072 3133 3194 3255 3316 3377 3438 18 79 140 201 262 323 384 445 506 567 628 689 750
871 932 993 1054 1115 1176 1237 1298 1300 1361 1422 1483 1544 1605 1666 1727 1788 1849 1910 1971 2032 2093 2154 2215 2276 2337 2398 2459 2520 2581 2642 2703 2764 2825 2886 2947 3008 3010 3071 3132 3193 3254 3315 3376 3437 17 78 139 200 261 322 383 444 505 566 627 688 749 810
931 992 1053 1114 1175 1236 1297 1299 1360 1421 1482 1543 1604 1665 1726 1787 1848 1909 1970 2031 2092 2153 2214 2275 2336 2397 2458 2519 2580 2641 2702 2763 2824 2885 2946 3007 3068 3070 3131 3192 3253 3314 3375 3436 16 77 138 199 260 321 382 443 504 565 626 687 748 809 870
991 1052 1113 1174 1235 1296 1357 1359 1420 1481 1542 1603 1664 1725 1786 1847 1908 1969 2030 2091 2152 2213 2274 2335 2396 2457 2518 2579 2640 2701 2762 2823 2884 2945 3006 3067 3069 3130 3191 3252 3313 3374 3435 15 76 137 198 259 320 381 442 503 564 625 686 747 808 869 930
1051 1112 1173 1234 1295 1356 1358 1419 1480 1541 1602 1663 1724 1785 1846 1907 1968 2029 2090 2151 2212 2273 2334 2395 2456 2517 2578 2639 2700 2761 2822 2883 2944 3005 3066 3127 3129 3190 3251 3312 3373 3434 14 75 136 197 258 319 380 441 502 563 624 685 746 807 868 929 990
1111 1172 1233 1294 1355 1416 1418 1479 1540 1601 1662 1723 1784 1845 1906 1967 2028 2089 2150 2211 2272 2333 2394 2455 2516 2577 2638 2699 2760 2821 2882 2943 3004 3065 3126 3128 3189 3250 3311 3372 3433 13 74 135 196 257 318 379 440 501 562 623 684 745 806 867 928 989 1050
1171 1232 1293 1354 1415 1417 1478 1539 1600 1661 1722 1783 1844 1905 1966 2027 2088 2149 2210 2271 2332 2393 2454 2515 2576 2637 2698 2759 2820 2881 2942 3003 3064 3125 3186 3188 3249 3310 3371 3432 12 73 134 195 256 317 378 439 500 561 622 683 744 805 866 927 988 1049 1110
1231 1292 1353 1414 1475 1477 1538 1599 1660 1721 1782 1843 1904 1965 2026 2087 2148 2209 2270 2331 2392 2453 2514 2575 2636 2697 2758 2819 2880 2941 3002 3063 3124 3185 3187 3248 3309 3370 3431 11 72 133 194 255 316 377 438 499 560 621 682 743 804 865 926 987 1048 1109 1170
1291 1352 1413 1474 1476 1537 1598 1659 1720 1781 1842 1903 1964 2025 2086 2147 2208 2269 2330 2391 2452 2513 2574 2635 2696 2757 2818 2879 2940 3001 3062 3123 3184 3245 3247 3308 3369 3430 10 71 132 193 254 315 376 437 498 559 620 681 742 803 864 925 986 1047 1108 1169 1230
1351 1412 1473 1534 1536 1597 1658 1719 1780 1841 1902 1963 2024 2085 2146 2207 2268 2329 2390 2451 2512 2573 2634 2695 2756 2817 2878 2939 3000 3061 3122 3183 3244 3246 3307 3368 3429 9 70 131 192 253 314 375 436 497 558 619 680 741 802 863 924 985 1046 1107 1168 1229 1290
1411 1472 1533 1535 1596 1657 1718 1779 1840 1901 1962 2023 2084 2145 2206 2267 2328 2389 2450 2511 2572 2633 2694 2755 2816 2877 2938 2999 3060 3121 3182 3243 3304 3306 3367 3428 8 69 130 191 252 313 374 435 496 557 618 679 740 801 862 923 984 1045 1106 1167 1228 1289 1350
1471 1532 1593 1595 1656 1717 1778 1839 1900 1961 2022 2083 2144 2205 2266 2327 2388 2449 2510 2571 2632 2693 2754 2815 2876 2937 2998 3059 3120 3181 3242 3303 3305 3366 3427 7 68 129 190 251 312 373 434 495 556 617 678 739 800 861 922 983 1044 1105 1166 1227 1288 1349 1410
1531 1592 1594 1655 1716 1777 1838 1899 1960 2021 2082 2143 2204 2265 2326 2387 2448 2509 2570 2631 2692 2753 2814 2875 2936 2997 3058 3119 3180 3241 3302 3363 3365 3426 6 67 128 189 250 311 372 433 494 555 616 677 738 799 860 921 982 1043 1104 1165 1226 1287 1348 1409 1470
1591 1652 1654 1715 1776 1837 1898 1959 2020 2081 2142 2203 2264 2325 2386 2447 2508 2569 2630 2691 2752 2813 2874 2935 2996 3057 3118 3179 3240 3301 3362 3364 3425 5 66 127 188 249 310 371 432 493 554 615 676 737 798 859 920 981 1042 1103 1164 1225 1286 1347 1408 1469 1530
1651 1653 1714 1775 1836 1897 1958 2019 2080 2141 2202 2263 2324 2385 2446 2507 2568 2629 2690 2751 2812 2873 2934 2995 3056 3117 3178 3239 3300 3361 3422 3424 4 65 126 187 248 309 370 431 492 553 614 675 736 797 858 919 980 1041 1102 1163 1224 1285 1346 1407 1468 1529 1590
1711 1713 1774 1835 1896 1957 2018 2079 2140 2201 2262 2323 2384 2445 2506 2567 2628 2689 2750 2811 2872 2933 2994 3055 3116 3177 3238 3299 3360 3421 3423 3 64 125 186 247 308 369 430 491 552 613 674 735 796 857 918 979 1040 1101 1162 1223 1284 1345 1406 1467 1528 1589 1650
1712 1773 1834 1895 1956 2017 2078 2139 2200 2261 2322 2383 2444 2505 2566 2627 2688 2749 2810 2871 2932 2993 3054 3115 3176 3237 3298 3359 3420 3481 2 63 124 185 246 307 368 429 490 551 612 673 734 795 856 917 978 1039 1100 1161 1222 1283 1344 1405 1466 1527 1588 1649 1710


Please
Support Our Site



buy
Amazing Math Whiz
products from
our online store



Many other
Amazing Messages
are available

Please visit
www.MAZES.com/cp/
for details

How to Make Your Own Odd-Size Magic Square

  1. Draw a square with any odd number of rows and columns.
  2. Put your first number in the MIDDLE square of the TOP row.
  3. Move UP and to the RIGHT to find the position for your next number, but ...
    • if the next "position" is ABOVE a column, go to BOTTOM of that column (you can see a sample of this movement by looking at how we moved from 1 to 2 in the square above).
    • if the next "position" is to the RIGHT of a row, go to LEFT of that row (you can see this movement between (30) and (31) above).
    • if the next cell is already filled in, drop down to the cell below the number you just filled in for the next number (you can see this when you look at how we moved from 59 to the next number above).
    • if the next cell is both ABOVE and to the RIGHT of the entire square, drop down to the cell below the number you just filled in for your next number (you can see this if you look at (1770) and the next number).
  4. Print your NEXT number into the new square you just moved to.
  5. Repeat steps 3-4 until the entire square is full.
  6. You can see how it works by printing this page and drawing arrows to see how it worked when I created this magic square
This Magic Square was created by John Knoderer, a webmaster and computer programmer who is available to telecommute to your location.

If you found this page useful, and especially if you printed this page to distribute to students, we invite you to send a suitable donation to John (address below) or PayPal your donation to Donations (at) Mazes.com.

You can find more of John's puzzling materials at www.MAZES.com and at www.GodLovesEveryone.org. You can reach John at Webmaster (at) Mazes.com.

Fine Print: If you print and duplicate these magic squares for classroom use or other multiple copy use, please send a payment of $(however much you think this is worth) to the author. John puts a GREAT DEAL of time into creating and posting materials to the internet for you to use (and enjoy). Your donations will help pay bills and keep new materials coming your way.

Send your donations to:

John Knoderer
www.MAZES.com
P O Box 235
Sulphur Springs, AR 72768 USA

www.MAZES.com
www.GodLovesEveryone.org
www.DriverExam.org

E-mail the webmaster: webmaster (at) mazes.com

The contents of this page are copyright 2005 by the author. However, we recognize that teachers may wish to download and use our materials with their students. We give that permission, as long as the teacher sends what they believe to be a fair donation to the author each time the material is used.

 We also have other
Amazing Message
stores.

Click each image to see
many amazing choices


Amazing Teacher


Amazing Student


Amazing Student


Amazing Reader


Amazing Artist