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 65x65 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (137345)

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 65 by 65 magic square shown below has a magic sum equal to 137345.

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 65-by-65 Magic Square

(Magic Sum = 137345)

Books about
Magic Squares
at Amazon.co.UK


Support Our Site
by purchasing our
Amazing Math Whiz
products

and other
Amazing Messages

2147 2214 2281 2348 2415 2482 2549 2616 2683 2750 2817 2884 2951 3018 3085 3152 3219 3286 3353 3420 3487 3554 3621 3688 3755 3822 3889 3956 4023 4090 4157 4224 1 68 135 202 269 336 403 470 537 604 671 738 805 872 939 1006 1073 1140 1207 1274 1341 1408 1475 1542 1609 1676 1743 1810 1877 1944 2011 2078 2145
2213 2280 2347 2414 2481 2548 2615 2682 2749 2816 2883 2950 3017 3084 3151 3218 3285 3352 3419 3486 3553 3620 3687 3754 3821 3888 3955 4022 4089 4156 4223 65 67 134 201 268 335 402 469 536 603 670 737 804 871 938 1005 1072 1139 1206 1273 1340 1407 1474 1541 1608 1675 1742 1809 1876 1943 2010 2077 2144 2146
2279 2346 2413 2480 2547 2614 2681 2748 2815 2882 2949 3016 3083 3150 3217 3284 3351 3418 3485 3552 3619 3686 3753 3820 3887 3954 4021 4088 4155 4222 64 66 133 200 267 334 401 468 535 602 669 736 803 870 937 1004 1071 1138 1205 1272 1339 1406 1473 1540 1607 1674 1741 1808 1875 1942 2009 2076 2143 2210 2212
2345 2412 2479 2546 2613 2680 2747 2814 2881 2948 3015 3082 3149 3216 3283 3350 3417 3484 3551 3618 3685 3752 3819 3886 3953 4020 4087 4154 4221 63 130 132 199 266 333 400 467 534 601 668 735 802 869 936 1003 1070 1137 1204 1271 1338 1405 1472 1539 1606 1673 1740 1807 1874 1941 2008 2075 2142 2209 2211 2278
2411 2478 2545 2612 2679 2746 2813 2880 2947 3014 3081 3148 3215 3282 3349 3416 3483 3550 3617 3684 3751 3818 3885 3952 4019 4086 4153 4220 62 129 131 198 265 332 399 466 533 600 667 734 801 868 935 1002 1069 1136 1203 1270 1337 1404 1471 1538 1605 1672 1739 1806 1873 1940 2007 2074 2141 2208 2275 2277 2344
2477 2544 2611 2678 2745 2812 2879 2946 3013 3080 3147 3214 3281 3348 3415 3482 3549 3616 3683 3750 3817 3884 3951 4018 4085 4152 4219 61 128 195 197 264 331 398 465 532 599 666 733 800 867 934 1001 1068 1135 1202 1269 1336 1403 1470 1537 1604 1671 1738 1805 1872 1939 2006 2073 2140 2207 2274 2276 2343 2410
2543 2610 2677 2744 2811 2878 2945 3012 3079 3146 3213 3280 3347 3414 3481 3548 3615 3682 3749 3816 3883 3950 4017 4084 4151 4218 60 127 194 196 263 330 397 464 531 598 665 732 799 866 933 1000 1067 1134 1201 1268 1335 1402 1469 1536 1603 1670 1737 1804 1871 1938 2005 2072 2139 2206 2273 2340 2342 2409 2476
2609 2676 2743 2810 2877 2944 3011 3078 3145 3212 3279 3346 3413 3480 3547 3614 3681 3748 3815 3882 3949 4016 4083 4150 4217 59 126 193 260 262 329 396 463 530 597 664 731 798 865 932 999 1066 1133 1200 1267 1334 1401 1468 1535 1602 1669 1736 1803 1870 1937 2004 2071 2138 2205 2272 2339 2341 2408 2475 2542
2675 2742 2809 2876 2943 3010 3077 3144 3211 3278 3345 3412 3479 3546 3613 3680 3747 3814 3881 3948 4015 4082 4149 4216 58 125 192 259 261 328 395 462 529 596 663 730 797 864 931 998 1065 1132 1199 1266 1333 1400 1467 1534 1601 1668 1735 1802 1869 1936 2003 2070 2137 2204 2271 2338 2405 2407 2474 2541 2608
2741 2808 2875 2942 3009 3076 3143 3210 3277 3344 3411 3478 3545 3612 3679 3746 3813 3880 3947 4014 4081 4148 4215 57 124 191 258 325 327 394 461 528 595 662 729 796 863 930 997 1064 1131 1198 1265 1332 1399 1466 1533 1600 1667 1734 1801 1868 1935 2002 2069 2136 2203 2270 2337 2404 2406 2473 2540 2607 2674
2807 2874 2941 3008 3075 3142 3209 3276 3343 3410 3477 3544 3611 3678 3745 3812 3879 3946 4013 4080 4147 4214 56 123 190 257 324 326 393 460 527 594 661 728 795 862 929 996 1063 1130 1197 1264 1331 1398 1465 1532 1599 1666 1733 1800 1867 1934 2001 2068 2135 2202 2269 2336 2403 2470 2472 2539 2606 2673 2740
2873 2940 3007 3074 3141 3208 3275 3342 3409 3476 3543 3610 3677 3744 3811 3878 3945 4012 4079 4146 4213 55 122 189 256 323 390 392 459 526 593 660 727 794 861 928 995 1062 1129 1196 1263 1330 1397 1464 1531 1598 1665 1732 1799 1866 1933 2000 2067 2134 2201 2268 2335 2402 2469 2471 2538 2605 2672 2739 2806
2939 3006 3073 3140 3207 3274 3341 3408 3475 3542 3609 3676 3743 3810 3877 3944 4011 4078 4145 4212 54 121 188 255 322 389 391 458 525 592 659 726 793 860 927 994 1061 1128 1195 1262 1329 1396 1463 1530 1597 1664 1731 1798 1865 1932 1999 2066 2133 2200 2267 2334 2401 2468 2535 2537 2604 2671 2738 2805 2872
3005 3072 3139 3206 3273 3340 3407 3474 3541 3608 3675 3742 3809 3876 3943 4010 4077 4144 4211 53 120 187 254 321 388 455 457 524 591 658 725 792 859 926 993 1060 1127 1194 1261 1328 1395 1462 1529 1596 1663 1730 1797 1864 1931 1998 2065 2132 2199 2266 2333 2400 2467 2534 2536 2603 2670 2737 2804 2871 2938
3071 3138 3205 3272 3339 3406 3473 3540 3607 3674 3741 3808 3875 3942 4009 4076 4143 4210 52 119 186 253 320 387 454 456 523 590 657 724 791 858 925 992 1059 1126 1193 1260 1327 1394 1461 1528 1595 1662 1729 1796 1863 1930 1997 2064 2131 2198 2265 2332 2399 2466 2533 2600 2602 2669 2736 2803 2870 2937 3004
3137 3204 3271 3338 3405 3472 3539 3606 3673 3740 3807 3874 3941 4008 4075 4142 4209 51 118 185 252 319 386 453 520 522 589 656 723 790 857 924 991 1058 1125 1192 1259 1326 1393 1460 1527 1594 1661 1728 1795 1862 1929 1996 2063 2130 2197 2264 2331 2398 2465 2532 2599 2601 2668 2735 2802 2869 2936 3003 3070
3203 3270 3337 3404 3471 3538 3605 3672 3739 3806 3873 3940 4007 4074 4141 4208 50 117 184 251 318 385 452 519 521 588 655 722 789 856 923 990 1057 1124 1191 1258 1325 1392 1459 1526 1593 1660 1727 1794 1861 1928 1995 2062 2129 2196 2263 2330 2397 2464 2531 2598 2665 2667 2734 2801 2868 2935 3002 3069 3136
3269 3336 3403 3470 3537 3604 3671 3738 3805 3872 3939 4006 4073 4140 4207 49 116 183 250 317 384 451 518 585 587 654 721 788 855 922 989 1056 1123 1190 1257 1324 1391 1458 1525 1592 1659 1726 1793 1860 1927 1994 2061 2128 2195 2262 2329 2396 2463 2530 2597 2664 2666 2733 2800 2867 2934 3001 3068 3135 3202
3335 3402 3469 3536 3603 3670 3737 3804 3871 3938 4005 4072 4139 4206 48 115 182 249 316 383 450 517 584 586 653 720 787 854 921 988 1055 1122 1189 1256 1323 1390 1457 1524 1591 1658 1725 1792 1859 1926 1993 2060 2127 2194 2261 2328 2395 2462 2529 2596 2663 2730 2732 2799 2866 2933 3000 3067 3134 3201 3268
3401 3468 3535 3602 3669 3736 3803 3870 3937 4004 4071 4138 4205 47 114 181 248 315 382 449 516 583 650 652 719 786 853 920 987 1054 1121 1188 1255 1322 1389 1456 1523 1590 1657 1724 1791 1858 1925 1992 2059 2126 2193 2260 2327 2394 2461 2528 2595 2662 2729 2731 2798 2865 2932 2999 3066 3133 3200 3267 3334
3467 3534 3601 3668 3735 3802 3869 3936 4003 4070 4137 4204 46 113 180 247 314 381 448 515 582 649 651 718 785 852 919 986 1053 1120 1187 1254 1321 1388 1455 1522 1589 1656 1723 1790 1857 1924 1991 2058 2125 2192 2259 2326 2393 2460 2527 2594 2661 2728 2795 2797 2864 2931 2998 3065 3132 3199 3266 3333 3400
3533 3600 3667 3734 3801 3868 3935 4002 4069 4136 4203 45 112 179 246 313 380 447 514 581 648 715 717 784 851 918 985 1052 1119 1186 1253 1320 1387 1454 1521 1588 1655 1722 1789 1856 1923 1990 2057 2124 2191 2258 2325 2392 2459 2526 2593 2660 2727 2794 2796 2863 2930 2997 3064 3131 3198 3265 3332 3399 3466
3599 3666 3733 3800 3867 3934 4001 4068 4135 4202 44 111 178 245 312 379 446 513 580 647 714 716 783 850 917 984 1051 1118 1185 1252 1319 1386 1453 1520 1587 1654 1721 1788 1855 1922 1989 2056 2123 2190 2257 2324 2391 2458 2525 2592 2659 2726 2793 2860 2862 2929 2996 3063 3130 3197 3264 3331 3398 3465 3532
3665 3732 3799 3866 3933 4000 4067 4134 4201 43 110 177 244 311 378 445 512 579 646 713 780 782 849 916 983 1050 1117 1184 1251 1318 1385 1452 1519 1586 1653 1720 1787 1854 1921 1988 2055 2122 2189 2256 2323 2390 2457 2524 2591 2658 2725 2792 2859 2861 2928 2995 3062 3129 3196 3263 3330 3397 3464 3531 3598
3731 3798 3865 3932 3999 4066 4133 4200 42 109 176 243 310 377 444 511 578 645 712 779 781 848 915 982 1049 1116 1183 1250 1317 1384 1451 1518 1585 1652 1719 1786 1853 1920 1987 2054 2121 2188 2255 2322 2389 2456 2523 2590 2657 2724 2791 2858 2925 2927 2994 3061 3128 3195 3262 3329 3396 3463 3530 3597 3664
3797 3864 3931 3998 4065 4132 4199 41 108 175 242 309 376 443 510 577 644 711 778 845 847 914 981 1048 1115 1182 1249 1316 1383 1450 1517 1584 1651 1718 1785 1852 1919 1986 2053 2120 2187 2254 2321 2388 2455 2522 2589 2656 2723 2790 2857 2924 2926 2993 3060 3127 3194 3261 3328 3395 3462 3529 3596 3663 3730
3863 3930 3997 4064 4131 4198 40 107 174 241 308 375 442 509 576 643 710 777 844 846 913 980 1047 1114 1181 1248 1315 1382 1449 1516 1583 1650 1717 1784 1851 1918 1985 2052 2119 2186 2253 2320 2387 2454 2521 2588 2655 2722 2789 2856 2923 2990 2992 3059 3126 3193 3260 3327 3394 3461 3528 3595 3662 3729 3796
3929 3996 4063 4130 4197 39 106 173 240 307 374 441 508 575 642 709 776 843 910 912 979 1046 1113 1180 1247 1314 1381 1448 1515 1582 1649 1716 1783 1850 1917 1984 2051 2118 2185 2252 2319 2386 2453 2520 2587 2654 2721 2788 2855 2922 2989 2991 3058 3125 3192 3259 3326 3393 3460 3527 3594 3661 3728 3795 3862
3995 4062 4129 4196 38 105 172 239 306 373 440 507 574 641 708 775 842 909 911 978 1045 1112 1179 1246 1313 1380 1447 1514 1581 1648 1715 1782 1849 1916 1983 2050 2117 2184 2251 2318 2385 2452 2519 2586 2653 2720 2787 2854 2921 2988 3055 3057 3124 3191 3258 3325 3392 3459 3526 3593 3660 3727 3794 3861 3928
4061 4128 4195 37 104 171 238 305 372 439 506 573 640 707 774 841 908 975 977 1044 1111 1178 1245 1312 1379 1446 1513 1580 1647 1714 1781 1848 1915 1982 2049 2116 2183 2250 2317 2384 2451 2518 2585 2652 2719 2786 2853 2920 2987 3054 3056 3123 3190 3257 3324 3391 3458 3525 3592 3659 3726 3793 3860 3927 3994
4127 4194 36 103 170 237 304 371 438 505 572 639 706 773 840 907 974 976 1043 1110 1177 1244 1311 1378 1445 1512 1579 1646 1713 1780 1847 1914 1981 2048 2115 2182 2249 2316 2383 2450 2517 2584 2651 2718 2785 2852 2919 2986 3053 3120 3122 3189 3256 3323 3390 3457 3524 3591 3658 3725 3792 3859 3926 3993 4060
4193 35 102 169 236 303 370 437 504 571 638 705 772 839 906 973 1040 1042 1109 1176 1243 1310 1377 1444 1511 1578 1645 1712 1779 1846 1913 1980 2047 2114 2181 2248 2315 2382 2449 2516 2583 2650 2717 2784 2851 2918 2985 3052 3119 3121 3188 3255 3322 3389 3456 3523 3590 3657 3724 3791 3858 3925 3992 4059 4126
34 101 168 235 302 369 436 503 570 637 704 771 838 905 972 1039 1041 1108 1175 1242 1309 1376 1443 1510 1577 1644 1711 1778 1845 1912 1979 2046 2113 2180 2247 2314 2381 2448 2515 2582 2649 2716 2783 2850 2917 2984 3051 3118 3185 3187 3254 3321 3388 3455 3522 3589 3656 3723 3790 3857 3924 3991 4058 4125 4192
100 167 234 301 368 435 502 569 636 703 770 837 904 971 1038 1105 1107 1174 1241 1308 1375 1442 1509 1576 1643 1710 1777 1844 1911 1978 2045 2112 2179 2246 2313 2380 2447 2514 2581 2648 2715 2782 2849 2916 2983 3050 3117 3184 3186 3253 3320 3387 3454 3521 3588 3655 3722 3789 3856 3923 3990 4057 4124 4191 33
166 233 300 367 434 501 568 635 702 769 836 903 970 1037 1104 1106 1173 1240 1307 1374 1441 1508 1575 1642 1709 1776 1843 1910 1977 2044 2111 2178 2245 2312 2379 2446 2513 2580 2647 2714 2781 2848 2915 2982 3049 3116 3183 3250 3252 3319 3386 3453 3520 3587 3654 3721 3788 3855 3922 3989 4056 4123 4190 32 99
232 299 366 433 500 567 634 701 768 835 902 969 1036 1103 1170 1172 1239 1306 1373 1440 1507 1574 1641 1708 1775 1842 1909 1976 2043 2110 2177 2244 2311 2378 2445 2512 2579 2646 2713 2780 2847 2914 2981 3048 3115 3182 3249 3251 3318 3385 3452 3519 3586 3653 3720 3787 3854 3921 3988 4055 4122 4189 31 98 165
298 365 432 499 566 633 700 767 834 901 968 1035 1102 1169 1171 1238 1305 1372 1439 1506 1573 1640 1707 1774 1841 1908 1975 2042 2109 2176 2243 2310 2377 2444 2511 2578 2645 2712 2779 2846 2913 2980 3047 3114 3181 3248 3315 3317 3384 3451 3518 3585 3652 3719 3786 3853 3920 3987 4054 4121 4188 30 97 164 231
364 431 498 565 632 699 766 833 900 967 1034 1101 1168 1235 1237 1304 1371 1438 1505 1572 1639 1706 1773 1840 1907 1974 2041 2108 2175 2242 2309 2376 2443 2510 2577 2644 2711 2778 2845 2912 2979 3046 3113 3180 3247 3314 3316 3383 3450 3517 3584 3651 3718 3785 3852 3919 3986 4053 4120 4187 29 96 163 230 297
430 497 564 631 698 765 832 899 966 1033 1100 1167 1234 1236 1303 1370 1437 1504 1571 1638 1705 1772 1839 1906 1973 2040 2107 2174 2241 2308 2375 2442 2509 2576 2643 2710 2777 2844 2911 2978 3045 3112 3179 3246 3313 3380 3382 3449 3516 3583 3650 3717 3784 3851 3918 3985 4052 4119 4186 28 95 162 229 296 363
496 563 630 697 764 831 898 965 1032 1099 1166 1233 1300 1302 1369 1436 1503 1570 1637 1704 1771 1838 1905 1972 2039 2106 2173 2240 2307 2374 2441 2508 2575 2642 2709 2776 2843 2910 2977 3044 3111 3178 3245 3312 3379 3381 3448 3515 3582 3649 3716 3783 3850 3917 3984 4051 4118 4185 27 94 161 228 295 362 429
562 629 696 763 830 897 964 1031 1098 1165 1232 1299 1301 1368 1435 1502 1569 1636 1703 1770 1837 1904 1971 2038 2105 2172 2239 2306 2373 2440 2507 2574 2641 2708 2775 2842 2909 2976 3043 3110 3177 3244 3311 3378 3445 3447 3514 3581 3648 3715 3782 3849 3916 3983 4050 4117 4184 26 93 160 227 294 361 428 495
628 695 762 829 896 963 1030 1097 1164 1231 1298 1365 1367 1434 1501 1568 1635 1702 1769 1836 1903 1970 2037 2104 2171 2238 2305 2372 2439 2506 2573 2640 2707 2774 2841 2908 2975 3042 3109 3176 3243 3310 3377 3444 3446 3513 3580 3647 3714 3781 3848 3915 3982 4049 4116 4183 25 92 159 226 293 360 427 494 561
694 761 828 895 962 1029 1096 1163 1230 1297 1364 1366 1433 1500 1567 1634 1701 1768 1835 1902 1969 2036 2103 2170 2237 2304 2371 2438 2505 2572 2639 2706 2773 2840 2907 2974 3041 3108 3175 3242 3309 3376 3443 3510 3512 3579 3646 3713 3780 3847 3914 3981 4048 4115 4182 24 91 158 225 292 359 426 493 560 627
760 827 894 961 1028 1095 1162 1229 1296 1363 1430 1432 1499 1566 1633 1700 1767 1834 1901 1968 2035 2102 2169 2236 2303 2370 2437 2504 2571 2638 2705 2772 2839 2906 2973 3040 3107 3174 3241 3308 3375 3442 3509 3511 3578 3645 3712 3779 3846 3913 3980 4047 4114 4181 23 90 157 224 291 358 425 492 559 626 693
826 893 960 1027 1094 1161 1228 1295 1362 1429 1431 1498 1565 1632 1699 1766 1833 1900 1967 2034 2101 2168 2235 2302 2369 2436 2503 2570 2637 2704 2771 2838 2905 2972 3039 3106 3173 3240 3307 3374 3441 3508 3575 3577 3644 3711 3778 3845 3912 3979 4046 4113 4180 22 89 156 223 290 357 424 491 558 625 692 759
892 959 1026 1093 1160 1227 1294 1361 1428 1495 1497 1564 1631 1698 1765 1832 1899 1966 2033 2100 2167 2234 2301 2368 2435 2502 2569 2636 2703 2770 2837 2904 2971 3038 3105 3172 3239 3306 3373 3440 3507 3574 3576 3643 3710 3777 3844 3911 3978 4045 4112 4179 21 88 155 222 289 356 423 490 557 624 691 758 825
958 1025 1092 1159 1226 1293 1360 1427 1494 1496 1563 1630 1697 1764 1831 1898 1965 2032 2099 2166 2233 2300 2367 2434 2501 2568 2635 2702 2769 2836 2903 2970 3037 3104 3171 3238 3305 3372 3439 3506 3573 3640 3642 3709 3776 3843 3910 3977 4044 4111 4178 20 87 154 221 288 355 422 489 556 623 690 757 824 891
1024 1091 1158 1225 1292 1359 1426 1493 1560 1562 1629 1696 1763 1830 1897 1964 2031 2098 2165 2232 2299 2366 2433 2500 2567 2634 2701 2768 2835 2902 2969 3036 3103 3170 3237 3304 3371 3438 3505 3572 3639 3641 3708 3775 3842 3909 3976 4043 4110 4177 19 86 153 220 287 354 421 488 555 622 689 756 823 890 957
1090 1157 1224 1291 1358 1425 1492 1559 1561 1628 1695 1762 1829 1896 1963 2030 2097 2164 2231 2298 2365 2432 2499 2566 2633 2700 2767 2834 2901 2968 3035 3102 3169 3236 3303 3370 3437 3504 3571 3638 3705 3707 3774 3841 3908 3975 4042 4109 4176 18 85 152 219 286 353 420 487 554 621 688 755 822 889 956 1023
1156 1223 1290 1357 1424 1491 1558 1625 1627 1694 1761 1828 1895 1962 2029 2096 2163 2230 2297 2364 2431 2498 2565 2632 2699 2766 2833 2900 2967 3034 3101 3168 3235 3302 3369 3436 3503 3570 3637 3704 3706 3773 3840 3907 3974 4041 4108 4175 17 84 151 218 285 352 419 486 553 620 687 754 821 888 955 1022 1089
1222 1289 1356 1423 1490 1557 1624 1626 1693 1760 1827 1894 1961 2028 2095 2162 2229 2296 2363 2430 2497 2564 2631 2698 2765 2832 2899 2966 3033 3100 3167 3234 3301 3368 3435 3502 3569 3636 3703 3770 3772 3839 3906 3973 4040 4107 4174 16 83 150 217 284 351 418 485 552 619 686 753 820 887 954 1021 1088 1155
1288 1355 1422 1489 1556 1623 1690 1692 1759 1826 1893 1960 2027 2094 2161 2228 2295 2362 2429 2496 2563 2630 2697 2764 2831 2898 2965 3032 3099 3166 3233 3300 3367 3434 3501 3568 3635 3702 3769 3771 3838 3905 3972 4039 4106 4173 15 82 149 216 283 350 417 484 551 618 685 752 819 886 953 1020 1087 1154 1221
1354 1421 1488 1555 1622 1689 1691 1758 1825 1892 1959 2026 2093 2160 2227 2294 2361 2428 2495 2562 2629 2696 2763 2830 2897 2964 3031 3098 3165 3232 3299 3366 3433 3500 3567 3634 3701 3768 3835 3837 3904 3971 4038 4105 4172 14 81 148 215 282 349 416 483 550 617 684 751 818 885 952 1019 1086 1153 1220 1287
1420 1487 1554 1621 1688 1755 1757 1824 1891 1958 2025 2092 2159 2226 2293 2360 2427 2494 2561 2628 2695 2762 2829 2896 2963 3030 3097 3164 3231 3298 3365 3432 3499 3566 3633 3700 3767 3834 3836 3903 3970 4037 4104 4171 13 80 147 214 281 348 415 482 549 616 683 750 817 884 951 1018 1085 1152 1219 1286 1353
1486 1553 1620 1687 1754 1756 1823 1890 1957 2024 2091 2158 2225 2292 2359 2426 2493 2560 2627 2694 2761 2828 2895 2962 3029 3096 3163 3230 3297 3364 3431 3498 3565 3632 3699 3766 3833 3900 3902 3969 4036 4103 4170 12 79 146 213 280 347 414 481 548 615 682 749 816 883 950 1017 1084 1151 1218 1285 1352 1419
1552 1619 1686 1753 1820 1822 1889 1956 2023 2090 2157 2224 2291 2358 2425 2492 2559 2626 2693 2760 2827 2894 2961 3028 3095 3162 3229 3296 3363 3430 3497 3564 3631 3698 3765 3832 3899 3901 3968 4035 4102 4169 11 78 145 212 279 346 413 480 547 614 681 748 815 882 949 1016 1083 1150 1217 1284 1351 1418 1485
1618 1685 1752 1819 1821 1888 1955 2022 2089 2156 2223 2290 2357 2424 2491 2558 2625 2692 2759 2826 2893 2960 3027 3094 3161 3228 3295 3362 3429 3496 3563 3630 3697 3764 3831 3898 3965 3967 4034 4101 4168 10 77 144 211 278 345 412 479 546 613 680 747 814 881 948 1015 1082 1149 1216 1283 1350 1417 1484 1551
1684 1751 1818 1885 1887 1954 2021 2088 2155 2222 2289 2356 2423 2490 2557 2624 2691 2758 2825 2892 2959 3026 3093 3160 3227 3294 3361 3428 3495 3562 3629 3696 3763 3830 3897 3964 3966 4033 4100 4167 9 76 143 210 277 344 411 478 545 612 679 746 813 880 947 1014 1081 1148 1215 1282 1349 1416 1483 1550 1617
1750 1817 1884 1886 1953 2020 2087 2154 2221 2288 2355 2422 2489 2556 2623 2690 2757 2824 2891 2958 3025 3092 3159 3226 3293 3360 3427 3494 3561 3628 3695 3762 3829 3896 3963 4030 4032 4099 4166 8 75 142 209 276 343 410 477 544 611 678 745 812 879 946 1013 1080 1147 1214 1281 1348 1415 1482 1549 1616 1683
1816 1883 1950 1952 2019 2086 2153 2220 2287 2354 2421 2488 2555 2622 2689 2756 2823 2890 2957 3024 3091 3158 3225 3292 3359 3426 3493 3560 3627 3694 3761 3828 3895 3962 4029 4031 4098 4165 7 74 141 208 275 342 409 476 543 610 677 744 811 878 945 1012 1079 1146 1213 1280 1347 1414 1481 1548 1615 1682 1749
1882 1949 1951 2018 2085 2152 2219 2286 2353 2420 2487 2554 2621 2688 2755 2822 2889 2956 3023 3090 3157 3224 3291 3358 3425 3492 3559 3626 3693 3760 3827 3894 3961 4028 4095 4097 4164 6 73 140 207 274 341 408 475 542 609 676 743 810 877 944 1011 1078 1145 1212 1279 1346 1413 1480 1547 1614 1681 1748 1815
1948 2015 2017 2084 2151 2218 2285 2352 2419 2486 2553 2620 2687 2754 2821 2888 2955 3022 3089 3156 3223 3290 3357 3424 3491 3558 3625 3692 3759 3826 3893 3960 4027 4094 4096 4163 5 72 139 206 273 340 407 474 541 608 675 742 809 876 943 1010 1077 1144 1211 1278 1345 1412 1479 1546 1613 1680 1747 1814 1881
2014 2016 2083 2150 2217 2284 2351 2418 2485 2552 2619 2686 2753 2820 2887 2954 3021 3088 3155 3222 3289 3356 3423 3490 3557 3624 3691 3758 3825 3892 3959 4026 4093 4160 4162 4 71 138 205 272 339 406 473 540 607 674 741 808 875 942 1009 1076 1143 1210 1277 1344 1411 1478 1545 1612 1679 1746 1813 1880 1947
2080 2082 2149 2216 2283 2350 2417 2484 2551 2618 2685 2752 2819 2886 2953 3020 3087 3154 3221 3288 3355 3422 3489 3556 3623 3690 3757 3824 3891 3958 4025 4092 4159 4161 3 70 137 204 271 338 405 472 539 606 673 740 807 874 941 1008 1075 1142 1209 1276 1343 1410 1477 1544 1611 1678 1745 1812 1879 1946 2013
2081 2148 2215 2282 2349 2416 2483 2550 2617 2684 2751 2818 2885 2952 3019 3086 3153 3220 3287 3354 3421 3488 3555 3622 3689 3756 3823 3890 3957 4024 4091 4158 4225 2 69 136 203 270 337 404 471 538 605 672 739 806 873 940 1007 1074 1141 1208 1275 1342 1409 1476 1543 1610 1677 1744 1811 1878 1945 2012 2079


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 (33) and (34) 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 65 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 (2145) 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