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 63x63 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (125055)

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 63 by 63 magic square shown below has a magic sum equal to 125055.

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 63-by-63 Magic Square

(Magic Sum = 125055)

Books about
Magic Squares
at Amazon.co.UK


Support Our Site
by purchasing our
Amazing Math Whiz
products

and other
Amazing Messages

2018 2083 2148 2213 2278 2343 2408 2473 2538 2603 2668 2733 2798 2863 2928 2993 3058 3123 3188 3253 3318 3383 3448 3513 3578 3643 3708 3773 3838 3903 3968 1 66 131 196 261 326 391 456 521 586 651 716 781 846 911 976 1041 1106 1171 1236 1301 1366 1431 1496 1561 1626 1691 1756 1821 1886 1951 2016
2082 2147 2212 2277 2342 2407 2472 2537 2602 2667 2732 2797 2862 2927 2992 3057 3122 3187 3252 3317 3382 3447 3512 3577 3642 3707 3772 3837 3902 3967 63 65 130 195 260 325 390 455 520 585 650 715 780 845 910 975 1040 1105 1170 1235 1300 1365 1430 1495 1560 1625 1690 1755 1820 1885 1950 2015 2017
2146 2211 2276 2341 2406 2471 2536 2601 2666 2731 2796 2861 2926 2991 3056 3121 3186 3251 3316 3381 3446 3511 3576 3641 3706 3771 3836 3901 3966 62 64 129 194 259 324 389 454 519 584 649 714 779 844 909 974 1039 1104 1169 1234 1299 1364 1429 1494 1559 1624 1689 1754 1819 1884 1949 2014 2079 2081
2210 2275 2340 2405 2470 2535 2600 2665 2730 2795 2860 2925 2990 3055 3120 3185 3250 3315 3380 3445 3510 3575 3640 3705 3770 3835 3900 3965 61 126 128 193 258 323 388 453 518 583 648 713 778 843 908 973 1038 1103 1168 1233 1298 1363 1428 1493 1558 1623 1688 1753 1818 1883 1948 2013 2078 2080 2145
2274 2339 2404 2469 2534 2599 2664 2729 2794 2859 2924 2989 3054 3119 3184 3249 3314 3379 3444 3509 3574 3639 3704 3769 3834 3899 3964 60 125 127 192 257 322 387 452 517 582 647 712 777 842 907 972 1037 1102 1167 1232 1297 1362 1427 1492 1557 1622 1687 1752 1817 1882 1947 2012 2077 2142 2144 2209
2338 2403 2468 2533 2598 2663 2728 2793 2858 2923 2988 3053 3118 3183 3248 3313 3378 3443 3508 3573 3638 3703 3768 3833 3898 3963 59 124 189 191 256 321 386 451 516 581 646 711 776 841 906 971 1036 1101 1166 1231 1296 1361 1426 1491 1556 1621 1686 1751 1816 1881 1946 2011 2076 2141 2143 2208 2273
2402 2467 2532 2597 2662 2727 2792 2857 2922 2987 3052 3117 3182 3247 3312 3377 3442 3507 3572 3637 3702 3767 3832 3897 3962 58 123 188 190 255 320 385 450 515 580 645 710 775 840 905 970 1035 1100 1165 1230 1295 1360 1425 1490 1555 1620 1685 1750 1815 1880 1945 2010 2075 2140 2205 2207 2272 2337
2466 2531 2596 2661 2726 2791 2856 2921 2986 3051 3116 3181 3246 3311 3376 3441 3506 3571 3636 3701 3766 3831 3896 3961 57 122 187 252 254 319 384 449 514 579 644 709 774 839 904 969 1034 1099 1164 1229 1294 1359 1424 1489 1554 1619 1684 1749 1814 1879 1944 2009 2074 2139 2204 2206 2271 2336 2401
2530 2595 2660 2725 2790 2855 2920 2985 3050 3115 3180 3245 3310 3375 3440 3505 3570 3635 3700 3765 3830 3895 3960 56 121 186 251 253 318 383 448 513 578 643 708 773 838 903 968 1033 1098 1163 1228 1293 1358 1423 1488 1553 1618 1683 1748 1813 1878 1943 2008 2073 2138 2203 2268 2270 2335 2400 2465
2594 2659 2724 2789 2854 2919 2984 3049 3114 3179 3244 3309 3374 3439 3504 3569 3634 3699 3764 3829 3894 3959 55 120 185 250 315 317 382 447 512 577 642 707 772 837 902 967 1032 1097 1162 1227 1292 1357 1422 1487 1552 1617 1682 1747 1812 1877 1942 2007 2072 2137 2202 2267 2269 2334 2399 2464 2529
2658 2723 2788 2853 2918 2983 3048 3113 3178 3243 3308 3373 3438 3503 3568 3633 3698 3763 3828 3893 3958 54 119 184 249 314 316 381 446 511 576 641 706 771 836 901 966 1031 1096 1161 1226 1291 1356 1421 1486 1551 1616 1681 1746 1811 1876 1941 2006 2071 2136 2201 2266 2331 2333 2398 2463 2528 2593
2722 2787 2852 2917 2982 3047 3112 3177 3242 3307 3372 3437 3502 3567 3632 3697 3762 3827 3892 3957 53 118 183 248 313 378 380 445 510 575 640 705 770 835 900 965 1030 1095 1160 1225 1290 1355 1420 1485 1550 1615 1680 1745 1810 1875 1940 2005 2070 2135 2200 2265 2330 2332 2397 2462 2527 2592 2657
2786 2851 2916 2981 3046 3111 3176 3241 3306 3371 3436 3501 3566 3631 3696 3761 3826 3891 3956 52 117 182 247 312 377 379 444 509 574 639 704 769 834 899 964 1029 1094 1159 1224 1289 1354 1419 1484 1549 1614 1679 1744 1809 1874 1939 2004 2069 2134 2199 2264 2329 2394 2396 2461 2526 2591 2656 2721
2850 2915 2980 3045 3110 3175 3240 3305 3370 3435 3500 3565 3630 3695 3760 3825 3890 3955 51 116 181 246 311 376 441 443 508 573 638 703 768 833 898 963 1028 1093 1158 1223 1288 1353 1418 1483 1548 1613 1678 1743 1808 1873 1938 2003 2068 2133 2198 2263 2328 2393 2395 2460 2525 2590 2655 2720 2785
2914 2979 3044 3109 3174 3239 3304 3369 3434 3499 3564 3629 3694 3759 3824 3889 3954 50 115 180 245 310 375 440 442 507 572 637 702 767 832 897 962 1027 1092 1157 1222 1287 1352 1417 1482 1547 1612 1677 1742 1807 1872 1937 2002 2067 2132 2197 2262 2327 2392 2457 2459 2524 2589 2654 2719 2784 2849
2978 3043 3108 3173 3238 3303 3368 3433 3498 3563 3628 3693 3758 3823 3888 3953 49 114 179 244 309 374 439 504 506 571 636 701 766 831 896 961 1026 1091 1156 1221 1286 1351 1416 1481 1546 1611 1676 1741 1806 1871 1936 2001 2066 2131 2196 2261 2326 2391 2456 2458 2523 2588 2653 2718 2783 2848 2913
3042 3107 3172 3237 3302 3367 3432 3497 3562 3627 3692 3757 3822 3887 3952 48 113 178 243 308 373 438 503 505 570 635 700 765 830 895 960 1025 1090 1155 1220 1285 1350 1415 1480 1545 1610 1675 1740 1805 1870 1935 2000 2065 2130 2195 2260 2325 2390 2455 2520 2522 2587 2652 2717 2782 2847 2912 2977
3106 3171 3236 3301 3366 3431 3496 3561 3626 3691 3756 3821 3886 3951 47 112 177 242 307 372 437 502 567 569 634 699 764 829 894 959 1024 1089 1154 1219 1284 1349 1414 1479 1544 1609 1674 1739 1804 1869 1934 1999 2064 2129 2194 2259 2324 2389 2454 2519 2521 2586 2651 2716 2781 2846 2911 2976 3041
3170 3235 3300 3365 3430 3495 3560 3625 3690 3755 3820 3885 3950 46 111 176 241 306 371 436 501 566 568 633 698 763 828 893 958 1023 1088 1153 1218 1283 1348 1413 1478 1543 1608 1673 1738 1803 1868 1933 1998 2063 2128 2193 2258 2323 2388 2453 2518 2583 2585 2650 2715 2780 2845 2910 2975 3040 3105
3234 3299 3364 3429 3494 3559 3624 3689 3754 3819 3884 3949 45 110 175 240 305 370 435 500 565 630 632 697 762 827 892 957 1022 1087 1152 1217 1282 1347 1412 1477 1542 1607 1672 1737 1802 1867 1932 1997 2062 2127 2192 2257 2322 2387 2452 2517 2582 2584 2649 2714 2779 2844 2909 2974 3039 3104 3169
3298 3363 3428 3493 3558 3623 3688 3753 3818 3883 3948 44 109 174 239 304 369 434 499 564 629 631 696 761 826 891 956 1021 1086 1151 1216 1281 1346 1411 1476 1541 1606 1671 1736 1801 1866 1931 1996 2061 2126 2191 2256 2321 2386 2451 2516 2581 2646 2648 2713 2778 2843 2908 2973 3038 3103 3168 3233
3362 3427 3492 3557 3622 3687 3752 3817 3882 3947 43 108 173 238 303 368 433 498 563 628 693 695 760 825 890 955 1020 1085 1150 1215 1280 1345 1410 1475 1540 1605 1670 1735 1800 1865 1930 1995 2060 2125 2190 2255 2320 2385 2450 2515 2580 2645 2647 2712 2777 2842 2907 2972 3037 3102 3167 3232 3297
3426 3491 3556 3621 3686 3751 3816 3881 3946 42 107 172 237 302 367 432 497 562 627 692 694 759 824 889 954 1019 1084 1149 1214 1279 1344 1409 1474 1539 1604 1669 1734 1799 1864 1929 1994 2059 2124 2189 2254 2319 2384 2449 2514 2579 2644 2709 2711 2776 2841 2906 2971 3036 3101 3166 3231 3296 3361
3490 3555 3620 3685 3750 3815 3880 3945 41 106 171 236 301 366 431 496 561 626 691 756 758 823 888 953 1018 1083 1148 1213 1278 1343 1408 1473 1538 1603 1668 1733 1798 1863 1928 1993 2058 2123 2188 2253 2318 2383 2448 2513 2578 2643 2708 2710 2775 2840 2905 2970 3035 3100 3165 3230 3295 3360 3425
3554 3619 3684 3749 3814 3879 3944 40 105 170 235 300 365 430 495 560 625 690 755 757 822 887 952 1017 1082 1147 1212 1277 1342 1407 1472 1537 1602 1667 1732 1797 1862 1927 1992 2057 2122 2187 2252 2317 2382 2447 2512 2577 2642 2707 2772 2774 2839 2904 2969 3034 3099 3164 3229 3294 3359 3424 3489
3618 3683 3748 3813 3878 3943 39 104 169 234 299 364 429 494 559 624 689 754 819 821 886 951 1016 1081 1146 1211 1276 1341 1406 1471 1536 1601 1666 1731 1796 1861 1926 1991 2056 2121 2186 2251 2316 2381 2446 2511 2576 2641 2706 2771 2773 2838 2903 2968 3033 3098 3163 3228 3293 3358 3423 3488 3553
3682 3747 3812 3877 3942 38 103 168 233 298 363 428 493 558 623 688 753 818 820 885 950 1015 1080 1145 1210 1275 1340 1405 1470 1535 1600 1665 1730 1795 1860 1925 1990 2055 2120 2185 2250 2315 2380 2445 2510 2575 2640 2705 2770 2835 2837 2902 2967 3032 3097 3162 3227 3292 3357 3422 3487 3552 3617
3746 3811 3876 3941 37 102 167 232 297 362 427 492 557 622 687 752 817 882 884 949 1014 1079 1144 1209 1274 1339 1404 1469 1534 1599 1664 1729 1794 1859 1924 1989 2054 2119 2184 2249 2314 2379 2444 2509 2574 2639 2704 2769 2834 2836 2901 2966 3031 3096 3161 3226 3291 3356 3421 3486 3551 3616 3681
3810 3875 3940 36 101 166 231 296 361 426 491 556 621 686 751 816 881 883 948 1013 1078 1143 1208 1273 1338 1403 1468 1533 1598 1663 1728 1793 1858 1923 1988 2053 2118 2183 2248 2313 2378 2443 2508 2573 2638 2703 2768 2833 2898 2900 2965 3030 3095 3160 3225 3290 3355 3420 3485 3550 3615 3680 3745
3874 3939 35 100 165 230 295 360 425 490 555 620 685 750 815 880 945 947 1012 1077 1142 1207 1272 1337 1402 1467 1532 1597 1662 1727 1792 1857 1922 1987 2052 2117 2182 2247 2312 2377 2442 2507 2572 2637 2702 2767 2832 2897 2899 2964 3029 3094 3159 3224 3289 3354 3419 3484 3549 3614 3679 3744 3809
3938 34 99 164 229 294 359 424 489 554 619 684 749 814 879 944 946 1011 1076 1141 1206 1271 1336 1401 1466 1531 1596 1661 1726 1791 1856 1921 1986 2051 2116 2181 2246 2311 2376 2441 2506 2571 2636 2701 2766 2831 2896 2961 2963 3028 3093 3158 3223 3288 3353 3418 3483 3548 3613 3678 3743 3808 3873
33 98 163 228 293 358 423 488 553 618 683 748 813 878 943 1008 1010 1075 1140 1205 1270 1335 1400 1465 1530 1595 1660 1725 1790 1855 1920 1985 2050 2115 2180 2245 2310 2375 2440 2505 2570 2635 2700 2765 2830 2895 2960 2962 3027 3092 3157 3222 3287 3352 3417 3482 3547 3612 3677 3742 3807 3872 3937
97 162 227 292 357 422 487 552 617 682 747 812 877 942 1007 1009 1074 1139 1204 1269 1334 1399 1464 1529 1594 1659 1724 1789 1854 1919 1984 2049 2114 2179 2244 2309 2374 2439 2504 2569 2634 2699 2764 2829 2894 2959 3024 3026 3091 3156 3221 3286 3351 3416 3481 3546 3611 3676 3741 3806 3871 3936 32
161 226 291 356 421 486 551 616 681 746 811 876 941 1006 1071 1073 1138 1203 1268 1333 1398 1463 1528 1593 1658 1723 1788 1853 1918 1983 2048 2113 2178 2243 2308 2373 2438 2503 2568 2633 2698 2763 2828 2893 2958 3023 3025 3090 3155 3220 3285 3350 3415 3480 3545 3610 3675 3740 3805 3870 3935 31 96
225 290 355 420 485 550 615 680 745 810 875 940 1005 1070 1072 1137 1202 1267 1332 1397 1462 1527 1592 1657 1722 1787 1852 1917 1982 2047 2112 2177 2242 2307 2372 2437 2502 2567 2632 2697 2762 2827 2892 2957 3022 3087 3089 3154 3219 3284 3349 3414 3479 3544 3609 3674 3739 3804 3869 3934 30 95 160
289 354 419 484 549 614 679 744 809 874 939 1004 1069 1134 1136 1201 1266 1331 1396 1461 1526 1591 1656 1721 1786 1851 1916 1981 2046 2111 2176 2241 2306 2371 2436 2501 2566 2631 2696 2761 2826 2891 2956 3021 3086 3088 3153 3218 3283 3348 3413 3478 3543 3608 3673 3738 3803 3868 3933 29 94 159 224
353 418 483 548 613 678 743 808 873 938 1003 1068 1133 1135 1200 1265 1330 1395 1460 1525 1590 1655 1720 1785 1850 1915 1980 2045 2110 2175 2240 2305 2370 2435 2500 2565 2630 2695 2760 2825 2890 2955 3020 3085 3150 3152 3217 3282 3347 3412 3477 3542 3607 3672 3737 3802 3867 3932 28 93 158 223 288
417 482 547 612 677 742 807 872 937 1002 1067 1132 1197 1199 1264 1329 1394 1459 1524 1589 1654 1719 1784 1849 1914 1979 2044 2109 2174 2239 2304 2369 2434 2499 2564 2629 2694 2759 2824 2889 2954 3019 3084 3149 3151 3216 3281 3346 3411 3476 3541 3606 3671 3736 3801 3866 3931 27 92 157 222 287 352
481 546 611 676 741 806 871 936 1001 1066 1131 1196 1198 1263 1328 1393 1458 1523 1588 1653 1718 1783 1848 1913 1978 2043 2108 2173 2238 2303 2368 2433 2498 2563 2628 2693 2758 2823 2888 2953 3018 3083 3148 3213 3215 3280 3345 3410 3475 3540 3605 3670 3735 3800 3865 3930 26 91 156 221 286 351 416
545 610 675 740 805 870 935 1000 1065 1130 1195 1260 1262 1327 1392 1457 1522 1587 1652 1717 1782 1847 1912 1977 2042 2107 2172 2237 2302 2367 2432 2497 2562 2627 2692 2757 2822 2887 2952 3017 3082 3147 3212 3214 3279 3344 3409 3474 3539 3604 3669 3734 3799 3864 3929 25 90 155 220 285 350 415 480
609 674 739 804 869 934 999 1064 1129 1194 1259 1261 1326 1391 1456 1521 1586 1651 1716 1781 1846 1911 1976 2041 2106 2171 2236 2301 2366 2431 2496 2561 2626 2691 2756 2821 2886 2951 3016 3081 3146 3211 3276 3278 3343 3408 3473 3538 3603 3668 3733 3798 3863 3928 24 89 154 219 284 349 414 479 544
673 738 803 868 933 998 1063 1128 1193 1258 1323 1325 1390 1455 1520 1585 1650 1715 1780 1845 1910 1975 2040 2105 2170 2235 2300 2365 2430 2495 2560 2625 2690 2755 2820 2885 2950 3015 3080 3145 3210 3275 3277 3342 3407 3472 3537 3602 3667 3732 3797 3862 3927 23 88 153 218 283 348 413 478 543 608
737 802 867 932 997 1062 1127 1192 1257 1322 1324 1389 1454 1519 1584 1649 1714 1779 1844 1909 1974 2039 2104 2169 2234 2299 2364 2429 2494 2559 2624 2689 2754 2819 2884 2949 3014 3079 3144 3209 3274 3339 3341 3406 3471 3536 3601 3666 3731 3796 3861 3926 22 87 152 217 282 347 412 477 542 607 672
801 866 931 996 1061 1126 1191 1256 1321 1386 1388 1453 1518 1583 1648 1713 1778 1843 1908 1973 2038 2103 2168 2233 2298 2363 2428 2493 2558 2623 2688 2753 2818 2883 2948 3013 3078 3143 3208 3273 3338 3340 3405 3470 3535 3600 3665 3730 3795 3860 3925 21 86 151 216 281 346 411 476 541 606 671 736
865 930 995 1060 1125 1190 1255 1320 1385 1387 1452 1517 1582 1647 1712 1777 1842 1907 1972 2037 2102 2167 2232 2297 2362 2427 2492 2557 2622 2687 2752 2817 2882 2947 3012 3077 3142 3207 3272 3337 3402 3404 3469 3534 3599 3664 3729 3794 3859 3924 20 85 150 215 280 345 410 475 540 605 670 735 800
929 994 1059 1124 1189 1254 1319 1384 1449 1451 1516 1581 1646 1711 1776 1841 1906 1971 2036 2101 2166 2231 2296 2361 2426 2491 2556 2621 2686 2751 2816 2881 2946 3011 3076 3141 3206 3271 3336 3401 3403 3468 3533 3598 3663 3728 3793 3858 3923 19 84 149 214 279 344 409 474 539 604 669 734 799 864
993 1058 1123 1188 1253 1318 1383 1448 1450 1515 1580 1645 1710 1775 1840 1905 1970 2035 2100 2165 2230 2295 2360 2425 2490 2555 2620 2685 2750 2815 2880 2945 3010 3075 3140 3205 3270 3335 3400 3465 3467 3532 3597 3662 3727 3792 3857 3922 18 83 148 213 278 343 408 473 538 603 668 733 798 863 928
1057 1122 1187 1252 1317 1382 1447 1512 1514 1579 1644 1709 1774 1839 1904 1969 2034 2099 2164 2229 2294 2359 2424 2489 2554 2619 2684 2749 2814 2879 2944 3009 3074 3139 3204 3269 3334 3399 3464 3466 3531 3596 3661 3726 3791 3856 3921 17 82 147 212 277 342 407 472 537 602 667 732 797 862 927 992
1121 1186 1251 1316 1381 1446 1511 1513 1578 1643 1708 1773 1838 1903 1968 2033 2098 2163 2228 2293 2358 2423 2488 2553 2618 2683 2748 2813 2878 2943 3008 3073 3138 3203 3268 3333 3398 3463 3528 3530 3595 3660 3725 3790 3855 3920 16 81 146 211 276 341 406 471 536 601 666 731 796 861 926 991 1056
1185 1250 1315 1380 1445 1510 1575 1577 1642 1707 1772 1837 1902 1967 2032 2097 2162 2227 2292 2357 2422 2487 2552 2617 2682 2747 2812 2877 2942 3007 3072 3137 3202 3267 3332 3397 3462 3527 3529 3594 3659 3724 3789 3854 3919 15 80 145 210 275 340 405 470 535 600 665 730 795 860 925 990 1055 1120
1249 1314 1379 1444 1509 1574 1576 1641 1706 1771 1836 1901 1966 2031 2096 2161 2226 2291 2356 2421 2486 2551 2616 2681 2746 2811 2876 2941 3006 3071 3136 3201 3266 3331 3396 3461 3526 3591 3593 3658 3723 3788 3853 3918 14 79 144 209 274 339 404 469 534 599 664 729 794 859 924 989 1054 1119 1184
1313 1378 1443 1508 1573 1638 1640 1705 1770 1835 1900 1965 2030 2095 2160 2225 2290 2355 2420 2485 2550 2615 2680 2745 2810 2875 2940 3005 3070 3135 3200 3265 3330 3395 3460 3525 3590 3592 3657 3722 3787 3852 3917 13 78 143 208 273 338 403 468 533 598 663 728 793 858 923 988 1053 1118 1183 1248
1377 1442 1507 1572 1637 1639 1704 1769 1834 1899 1964 2029 2094 2159 2224 2289 2354 2419 2484 2549 2614 2679 2744 2809 2874 2939 3004 3069 3134 3199 3264 3329 3394 3459 3524 3589 3654 3656 3721 3786 3851 3916 12 77 142 207 272 337 402 467 532 597 662 727 792 857 922 987 1052 1117 1182 1247 1312
1441 1506 1571 1636 1701 1703 1768 1833 1898 1963 2028 2093 2158 2223 2288 2353 2418 2483 2548 2613 2678 2743 2808 2873 2938 3003 3068 3133 3198 3263 3328 3393 3458 3523 3588 3653 3655 3720 3785 3850 3915 11 76 141 206 271 336 401 466 531 596 661 726 791 856 921 986 1051 1116 1181 1246 1311 1376
1505 1570 1635 1700 1702 1767 1832 1897 1962 2027 2092 2157 2222 2287 2352 2417 2482 2547 2612 2677 2742 2807 2872 2937 3002 3067 3132 3197 3262 3327 3392 3457 3522 3587 3652 3717 3719 3784 3849 3914 10 75 140 205 270 335 400 465 530 595 660 725 790 855 920 985 1050 1115 1180 1245 1310 1375 1440
1569 1634 1699 1764 1766 1831 1896 1961 2026 2091 2156 2221 2286 2351 2416 2481 2546 2611 2676 2741 2806 2871 2936 3001 3066 3131 3196 3261 3326 3391 3456 3521 3586 3651 3716 3718 3783 3848 3913 9 74 139 204 269 334 399 464 529 594 659 724 789 854 919 984 1049 1114 1179 1244 1309 1374 1439 1504
1633 1698 1763 1765 1830 1895 1960 2025 2090 2155 2220 2285 2350 2415 2480 2545 2610 2675 2740 2805 2870 2935 3000 3065 3130 3195 3260 3325 3390 3455 3520 3585 3650 3715 3780 3782 3847 3912 8 73 138 203 268 333 398 463 528 593 658 723 788 853 918 983 1048 1113 1178 1243 1308 1373 1438 1503 1568
1697 1762 1827 1829 1894 1959 2024 2089 2154 2219 2284 2349 2414 2479 2544 2609 2674 2739 2804 2869 2934 2999 3064 3129 3194 3259 3324 3389 3454 3519 3584 3649 3714 3779 3781 3846 3911 7 72 137 202 267 332 397 462 527 592 657 722 787 852 917 982 1047 1112 1177 1242 1307 1372 1437 1502 1567 1632
1761 1826 1828 1893 1958 2023 2088 2153 2218 2283 2348 2413 2478 2543 2608 2673 2738 2803 2868 2933 2998 3063 3128 3193 3258 3323 3388 3453 3518 3583 3648 3713 3778 3843 3845 3910 6 71 136 201 266 331 396 461 526 591 656 721 786 851 916 981 1046 1111 1176 1241 1306 1371 1436 1501 1566 1631 1696
1825 1890 1892 1957 2022 2087 2152 2217 2282 2347 2412 2477 2542 2607 2672 2737 2802 2867 2932 2997 3062 3127 3192 3257 3322 3387 3452 3517 3582 3647 3712 3777 3842 3844 3909 5 70 135 200 265 330 395 460 525 590 655 720 785 850 915 980 1045 1110 1175 1240 1305 1370 1435 1500 1565 1630 1695 1760
1889 1891 1956 2021 2086 2151 2216 2281 2346 2411 2476 2541 2606 2671 2736 2801 2866 2931 2996 3061 3126 3191 3256 3321 3386 3451 3516 3581 3646 3711 3776 3841 3906 3908 4 69 134 199 264 329 394 459 524 589 654 719 784 849 914 979 1044 1109 1174 1239 1304 1369 1434 1499 1564 1629 1694 1759 1824
1953 1955 2020 2085 2150 2215 2280 2345 2410 2475 2540 2605 2670 2735 2800 2865 2930 2995 3060 3125 3190 3255 3320 3385 3450 3515 3580 3645 3710 3775 3840 3905 3907 3 68 133 198 263 328 393 458 523 588 653 718 783 848 913 978 1043 1108 1173 1238 1303 1368 1433 1498 1563 1628 1693 1758 1823 1888
1954 2019 2084 2149 2214 2279 2344 2409 2474 2539 2604 2669 2734 2799 2864 2929 2994 3059 3124 3189 3254 3319 3384 3449 3514 3579 3644 3709 3774 3839 3904 3969 2 67 132 197 262 327 392 457 522 587 652 717 782 847 912 977 1042 1107 1172 1237 1302 1367 1432 1497 1562 1627 1692 1757 1822 1887 1952


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 (32) and (33) 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 63 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 (2016) 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