Introduction to Order-9 |
Cell designations & some of the features of Order-9 magic stars. |
Characteristics - Order-9 |
Adjacent complement pairs, numbers at points, three triangles, solutions with each point total, etc. |
Order 9A List of Basic Solutions |
A partial list of the 3014 basic solutions with complement number, complement pair number, point totals, and special feature remarks. |
Order 9B List of Basic Solutions |
A partial list of the 1676 basic solutions for this pattern. Same information as for pattern A. |
Order 9C List of Basic Solutions |
A partial list of the 1676 basic solutions for this pattern. Same information as for pattern A. |
Definitions |
Review magic star definitions and general features. Use Back button to return. |
Star Examples |
One example of each of 16 patterns, Orders 5 to 11. Use Back button to return |
Star Examples - 2 |
One example of each of 14 patterns, Orders 12 to 14. Use Back button to return |
Order-9 has three different patterns and is the smallest
order where the number of solutions is not the same for each pattern. Patterns A and B are continuous, pattern C consists of three superimposed triangles. (3 x 3 = 9). Pattern A 3014 solutions 2:12:43 running time Each solution contains the consecutive series of integers from 1 to 18. The sum of this series is 171, there are 9 lines with each cell appearing in 2 lines, so the magic constant (S) is (2 x 171)/9 = 38. Order-9B has no solutions with b = 2. |
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Order-9 Adjacent complement pairs | ||||||||||
Order-9A | Order-9B | Order-9C | ||||||||
Solution #'s | Pair # | Solution #'s | Pair # | Solution #'s | Pair # | |||||
2 | 3 | 2 | 4 | 5 | 4 | 7 | 8 | 5 | ||
1071 | 1072 | 978 | 99 | 100 | 66 | 36 | 37 | 29 | ||
1595 | 1596 | 1318 | 261 | 262 | 202 | 64 | 65 | 48 | ||
2076 | 2077 | 1467 | 303 | 304 | 242 | 66 | 67 | 49 | ||
2189 | 2190 | 1483 | 367 | 368 | 297 | 91 | 92 | 67 | ||
2192 | 2193 | 1484 | 491 | 492 | 387 | 101 | 102 | 129 | ||
2249 | 2250 | 1485 | 609 | 610 | 472 | 330 | 331 | 276 | ||
2254 | 2255 | 1486 | 638 | 639 | 496 | 535 | 536 | 434 | ||
883 | 884 | 659 | 983 | 984 | 701 | |||||
The last four pairs have sequential numbers but there are other solutions (belonging to other pairs) between them. | 902 | 903 | 668 | 1087 | 1088 | 751 | ||||
956 | 957 | 698 | 1279 | 1280 | 801 | |||||
1011 | 1012 | 714 | Numbers 48 and 49 are adjacent pairs. | |||||||
1068 | 1069 | 727 | ||||||||
1161 | 1162 | 779 | Last 3 are exactly 50 pair numbers apart. | |||||||
1166 | 1167 | 781 |
Order-9A |
Pattern 9A has different cell names and many
more solutions.then patterns 9B and 9C which have the same cell names and the same number
of basic solutions. Odd numbers at the points Low numbers at the points All odd orders have these types of solutions
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Odd | Even | 1 - 9 | 10 - 18 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
30 | 1548 | 1062 | 2993 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
31 | 1529 | 1063 | 2992 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
46 | 1524 | 1065 | 2991 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
52 | 1559 | 1067 | 2994 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
156 | 1592 | 1152 | 2998 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
170 | 1591 | 1153 | 2997 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
175 | 1587 | 1156 | 2996 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
177 | 1576 | 1157 | 2995 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
215 | 1949 | 1180 | 3012 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
231 | 1730 | 1183 | 3008 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
239 | 1623 | 1185 | 3001 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
387 | 1715 | 1259 | 3005 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
398 | 1714 | 1260 | 3004 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
399 | 1713 | 1261 | 3003 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
400 | 1706 | 1264 | 3002 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
408 | 1723 | 1267 | 3007 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
414 | 1720 | 1268 | 3006 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
439 | 1621 | 1273 | 3000 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
687 | 1858 | 1355 | 3010 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
689 | 1855 | 1356 | 3009 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
800 | 1889 | 1381 | 3011 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
995 | 1615 | 1435 | 2999 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1011 | 7056 | 1441 | 3014 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1253 | 1963 | 1500 | 3013 |
Order-9B consists of 3 super-imposed triangles. The points of these triangles all have the same value in 12 solutions (six complement pairs).
Solution Triangle Complement Triangle number point total number point total 103 31 110 26 106 28 108 29 187 23 1423 34 260 32 263 25 289 26 1098 31 638 30 639 27
Point Pattern Point Pattern Point Pattern Total A B C Total A B C Total A B C 45 24 5 5 59 10 16 16 73 44 33 33 46 10 3 3 60 37 9 9 74 51 24 24 47 7 9 9 61 30 9 9 75 62 37 37 48 14 6 6 62 28 15 15 76 42 22 22 49 9 6 6 63 30 16 16 77 61 38 38 50 16 1 1 64 31 11 11 78 90 47 47 51 17 3 3 65 25 18 18 79 60 43 43 52 10 1 1 66 52 17 17 80 51 35 35 53 7 12 12 67 23 19 19 81 114 36 36 54 18 6 6 68 39 38 38 82 48 41 41 55 8 5 5 69 35 30 30 83 47 56 56 56 5 0 0 70 49 23 23 84 95 36 36 57 11 6 6 71 42 34 34 85 55 37 37 58 11 5 5 72 89 33 33 Total solutions for the low half of the count is 1507 838 838 The high totals are the same as these, but in reverse order i.e. 86 matches with 85, 87 with 84,. . ., 126 with 45.
Sol.. | -------- cell value ----- Upper case indicates the points --------| Compl Pair Point Remarks # . A b c D e f G h i J k l M n O P Q R ment # Total 1 1 2 17 18 3 6 11 12 5 10 8 13 7 15 14 4 16 9 4 1 90 2 1 2 17 18 3 10 7 11 5 15 8 9 6 16 14 4 13 12 3 2 90 3 1 2 17 18 3 10 7 11 14 6 8 9 15 16 5 13 4 12 2 2 81 4 1 2 17 18 4 6 10 11 14 3 7 13 15 16 5 12 9 8 1 1 81 5 1 2 18 17 3 4 14 9 8 7 6 10 15 16 5 12 13 11 1521 3 95 6 1 2 18 17 3 4 14 12 5 7 8 13 10 15 11 6 16 9 1533 4 91 7 1 2 18 17 3 5 13 7 10 8 4 12 14 16 6 11 15 9 1518 5 94 8 1 2 18 17 3 5 13 10 11 4 7 15 12 16 8 9 14 6 1514 6 84 9 1 2 18 17 3 7 11 9 14 4 6 13 15 16 5 12 10 8 1516 7 83 10 1 2 18 17 3 8 10 14 9 5 11 15 7 16 13 4 12 6 1513 8 75 11 1 2 18 17 3 8 10 15 6 7 5 12 14 9 13 4 11 16 1564 9 93 12 1 2 18 17 3 11 7 9 6 16 4 8 10 14 12 5 13 15 1549 10 96 13 1 2 18 17 3 11 7 13 4 14 10 6 8 16 12 5 9 15 1527 11 88 14 1 2 18 17 3 11 7 14 4 13 10 6 9 15 12 5 8 16 1541 12 88 15 1 2 18 17 3 12 6 8 9 15 5 11 7 16 13 4 14 10 1520 13 87 16 1 2 18 17 3 13 5 9 16 8 4 11 15 14 7 10 6 12 1546 14 81 17 1 2 18 17 3 13 5 10 15 8 7 9 14 16 6 11 4 12 1522 15 78 18 1 2 18 17 3 13 5 15 8 10 12 7 9 16 11 6 4 14 1525 16 77 19 1 2 18 17 3 14 4 8 15 11 5 9 13 16 7 10 6 12 1523 17 81 20 1 2 18 17 3 14 4 10 11 13 7 6 12 16 8 9 5 15 1530 18 84 56 1 2 18 17 10 8 3 15 13 7 5 12 14 16 6 4 11 9 1517 54 72 57 1 3 16 18 2 5 13 15 4 6 7 11 14 9 12 8 10 17 74 55 99 142 1 3 18 16 11 9 2 15 14 7 6 12 13 17 5 4 10 8 2152 131 66 143 1 4 15 18 2 8 10 5 6 17 3 7 11 14 9 12 13 16 150 132 107 245 1 4 18 15 11 10 2 13 16 7 5 12 14 17 3 6 9 8 2513 228 65 246 1 5 14 18 2 7 11 6 4 17 3 10 8 12 13 9 16 15 263 229 108 377 1 5 18 14 11 10 3 17 12 6 9 8 15 16 2 7 4 13 2595 346 65 378 1 6 13 18 2 8 10 15 4 9 17 7 5 16 11 12 3 14 380 347 83 496 1 6 18 13 11 9 5 12 17 4 3 15 16 14 2 7 10 8 2289 460 66 497 1 7 12 18 2 3 15 14 4 5 10 17 6 9 16 8 13 11 513 461 93 659 1 7 18 12 14 9 3 17 5 13 8 6 11 16 4 2 10 15 2721 603 71 660 1 8 11 18 3 5 12 6 4 16 2 13 7 9 14 10 17 15 669 604 110 820 1 8 18 11 13 12 2 16 15 5 10 14 9 17 4 3 7 6 2949 748 48 821 1 9 10 18 12 5 3 13 7 15 8 4 11 16 2 14 6 17 554 503 87 969 1 9 18 10 15 5 8 17 7 6 4 12 16 11 2 3 13 14 2397 885 73 970 1 10 9 18 13 4 3 12 7 16 6 5 11 15 2 14 8 17 428 394 90 1070 1 10 18 9 15 6 8 14 11 5 4 17 12 13 3 2 16 7 2315 977 63 1071 1 11 8 18 5 9 6 2 16 14 3 17 4 13 10 15 12 7 1072 978 87 1186 1 11 18 8 15 10 5 14 13 6 9 16 7 17 3 2 12 4 2942 1080 48 1187 1 12 7 18 15 3 2 14 5 17 9 8 4 16 6 10 11 13 164 147 82 1293 1 12 18 7 15 11 5 16 4 13 9 6 10 14 2 3 8 17 2015 1164 66 1294 1 13 6 18 7 3 10 15 5 8 17 11 2 14 9 16 4 12 1252 1126 80 1384 1 13 18 6 15 10 7 12 11 8 9 16 5 17 3 2 14 4 2813 1237 50 1385 1 14 6 17 16 2 3 18 8 9 13 12 4 15 5 11 7 10 1609 1238 67 1453 1 14 18 5 12 17 4 11 7 16 10 9 3 15 6 2 8 13 2437 1286 58 1454 1 15 6 16 12 7 3 8 14 13 10 11 4 17 2 18 5 9 522 473 71 1503 1 15 18 4 10 13 11 14 6 7 17 9 5 16 2 8 3 12 2907 1310 53 1504 1 16 7 14 11 9 4 6 15 13 10 12 3 17 2 18 5 8 674 612 68 1512 1 16 15 6 11 9 12 14 8 4 18 13 3 17 2 10 5 7 2943 1312 50 1513 2 1 17 18 3 4 13 8 10 7 5 11 15 16 6 12 14 9 10 8 96 2148 2 15 11 10 6 14 8 1 17 12 9 13 4 16 3 18 5 7 334 303 69 2149 3 1 16 18 2 5 13 10 8 7 4 15 12 11 14 6 17 9 136 125 99 2511 3 13 10 12 8 1 17 14 2 5 18 9 6 15 4 16 7 11 1751 1368 81 2512 4 1 15 18 2 5 13 10 3 12 11 9 6 17 14 7 16 8 208 191 98 2721 4 11 14 9 2 10 17 5 1 15 12 3 8 13 6 16 7 18 659 603 100 2722 5 1 14 18 2 3 15 12 4 7 8 6 17 11 9 13 10 16 368 337 110 2829 5 11 15 7 3 10 18 2 1 17 9 4 8 13 6 14 12 16 906 823 103 2830 6 1 13 18 3 10 7 5 11 15 2 4 17 12 8 14 9 16 490 454 110 2887 6 7 14 11 1 9 17 2 3 16 5 4 13 10 8 15 12 18 1443 1276 116 2888 7 1 12 18 2 3 15 5 4 14 8 6 10 16 11 13 17 9 626 570 114 2948 7 6 10 15 2 3 18 5 1 14 8 4 12 11 9 17 13 16 1452 1285 121 2949 8 1 11 18 2 5 13 9 4 12 3 7 16 6 15 10 14 17 820 748 123 2972 8 6 15 9 1 11 17 3 2 16 4 5 13 7 12 10 14 18 1415 1254 117 2973 9 1 10 18 2 7 11 6 5 16 3 4 15 8 14 12 13 17 962 878 125 2990 9 6 11 12 1 7 18 2 3 15 5 4 14 8 10 16 13 17 1284 1155 124 2991 10 1 9 18 2 6 12 8 3 15 5 4 14 7 16 11 13 17 1065 972 126 Points are #'s 10 to 18 3005 10 3 7 18 4 5 11 2 8 17 1 6 14 9 12 15 16 13 1259 1131 126 3006 10 3 7 18 5 2 13 8 6 11 1 9 17 4 14 12 16 15 1268 1140 126 to the end 3007 10 3 7 18 6 1 13 9 4 12 2 8 16 5 14 11 17 15 1267 1139 126 3008 10 3 8 17 1 7 13 4 6 15 2 9 12 5 18 11 16 14 1183 1077 126 3009 10 4 6 18 2 7 11 3 8 16 1 9 12 5 17 13 15 14 1356 1211 126 3010 10 4 6 18 5 1 14 9 2 13 7 3 15 8 11 16 12 17 1355 1210 126 3011 10 4 9 15 2 7 14 3 8 13 1 6 18 5 11 16 12 17 1381 1234 126 3012 10 5 6 17 4 2 15 9 1 13 8 3 14 7 12 16 11 18 1180 1074 126 3013 10 5 7 16 1 4 17 2 8 11 3 9 15 6 12 18 14 13 1500 1308 126 3014 10 6 8 14 2 7 15 1 4 18 5 3 12 9 11 17 13 16 1441 1274 126
Sol.. | -------- cell value ----- Upper case indicates the points --------| Compl Pair Point Remarks # . A b c D e f G h i J k L m N o P Q R ment # Total 1 1 2 17 18 3 4 13 14 10 15 9 11 8 5 16 7 6 12 8 1 88 2 1 2 17 18 3 7 10 14 13 15 12 8 11 5 16 4 6 9 7 2 76 3 1 2 17 18 3 8 9 15 13 12 16 7 6 10 14 4 11 5 6 3 77 4 1 2 17 18 3 9 8 16 13 15 14 6 5 11 10 4 12 7 5 4 82 5 1 2 17 18 6 3 11 10 16 15 5 12 9 7 14 4 8 13 4 4 89 6 1 2 17 18 6 4 10 11 16 15 3 14 5 8 13 7 9 12 3 3 94 7 1 2 17 18 6 5 9 12 16 15 7 10 3 13 8 4 14 11 2 2 95 8 1 2 17 18 9 5 6 15 16 12 10 7 3 13 11 4 14 8 1 1 83 9 1 3 16 18 2 4 14 12 11 13 8 15 6 5 17 9 7 10 25 5 92 10 1 3 16 18 2 4 14 15 8 13 11 12 6 5 17 9 7 10 30 6 89 11 1 3 16 18 2 6 12 8 17 14 7 15 4 11 10 5 13 9 16 7 98 12 1 3 16 18 2 6 12 8 17 15 7 14 5 11 9 4 13 10 17 8 98 13 1 3 16 18 2 6 12 15 10 13 9 14 4 5 17 11 7 8 26 9 89 14 1 3 16 18 2 8 10 15 12 13 9 14 4 5 17 11 7 6 24 10 85 15 1 3 16 18 2 10 8 15 14 13 11 12 6 5 17 9 7 4 21 11 77 16 1 3 16 18 2 11 7 13 17 14 12 10 9 6 15 5 8 4 11 7 73 17 1 3 16 18 2 11 7 13 17 15 12 9 10 6 14 4 8 5 12 8 73 18 1 3 16 18 2 11 7 17 13 14 12 10 5 6 15 9 8 4 22 12 77 19 1 3 16 18 4 5 11 17 9 14 7 13 2 6 15 12 8 10 27 13 93 20 1 3 16 18 5 2 13 15 9 12 14 7 10 6 17 4 8 11 29 14 80 21 1 3 16 18 5 4 11 9 17 10 8 15 2 12 13 6 14 7 15 11 94 22 1 3 16 18 6 2 12 8 17 10 7 15 4 11 14 5 13 9 18 12 94 23 1 3 16 18 7 2 11 17 9 14 12 5 10 6 15 4 8 13 28 15 80 24 1 3 16 18 7 4 9 11 17 8 10 13 2 12 15 6 14 5 14 10 86 25 1 3 16 18 8 7 5 15 17 10 11 9 2 12 13 6 14 4 9 5 79 26 1 3 16 18 9 4 7 13 17 8 10 11 2 12 15 6 14 5 13 9 82 27 1 3 16 18 10 2 8 14 15 7 12 9 4 11 17 5 13 6 19 13 78 28 1 3 16 18 10 2 8 17 12 15 7 6 4 11 9 5 13 14 23 15 91 29 1 3 16 18 10 4 6 17 14 15 5 8 2 11 9 7 13 12 20 14 91 30 1 3 16 18 11 4 5 15 17 10 8 9 2 12 13 6 14 7 10 6 82 31 1 4 15 18 2 5 13 7 17 10 12 14 9 8 16 3 11 6 37 16 84 75 1 4 17 16 14 2 6 13 18 11 3 10 7 8 15 5 9 12 1152 49 78 76 1 5 14 18 2 3 15 10 12 13 6 17 7 4 16 9 8 11 107 50 96 147 1 5 17 15 14 6 3 16 18 13 7 4 10 8 12 2 9 11 1388 100 66 148 1 6 13 18 2 10 8 14 15 16 11 9 3 12 4 5 17 7 152 101 93 201 1 6 17 14 9 7 8 11 18 4 15 10 5 12 16 3 13 2 1534 146 67 202 1 7 12 18 4 2 14 10 13 6 17 11 8 9 16 3 15 5 204 147 82 259 1 7 17 13 14 5 6 15 16 10 2 12 8 3 18 9 4 11 1593 200 69 260 1 8 11 18 2 5 13 15 9 16 14 6 7 10 4 3 17 12 263 201 96 3 triangle point 300 1 8 17 12 10 3 13 6 18 7 5 16 2 14 9 4 15 11 1306 239 93 totals same 301 1 9 10 18 2 4 14 12 11 6 17 13 5 8 15 7 16 3 310 240 86 365 1 9 17 11 16 3 8 15 14 13 4 5 12 6 10 2 7 18 118 71 71 366 1 10 9 18 5 7 8 16 13 12 4 17 3 2 14 15 11 6 369 296 90 423 1 10 16 11 18 4 5 17 15 9 8 3 6 12 7 2 14 13 1580 338 70 424 1 11 8 18 3 2 15 10 12 14 4 17 5 6 7 9 16 13 425 339 109 490 1 11 17 9 18 3 8 15 14 5 2 13 4 6 16 10 7 12 1589 386 71 491 1 12 7 18 2 8 10 14 13 16 5 15 3 6 4 11 17 9 492 387 103 564 1 12 17 8 18 2 10 14 13 6 3 11 9 4 16 7 5 15 1442 439 67 565 1 13 6 18 11 2 7 14 16 5 10 12 9 3 17 8 15 4 295 234 73 608 1 13 17 7 16 11 4 15 18 2 12 8 6 9 14 5 10 3 1670 471 49 609 1 14 5 18 3 4 13 8 16 12 6 17 11 2 10 7 15 9 610 472 94 637 1 14 17 6 12 5 15 4 18 3 7 16 10 8 13 2 9 11 1250 495 71 638 1 15 4 18 2 7 11 10 16 14 9 13 12 3 6 5 17 8 639 496 90 3 triangle point 680 1 15 17 5 16 10 7 12 18 2 11 9 4 13 8 3 14 6 1576 533 60 totals same 681 1 16 7 14 13 9 2 17 18 10 3 12 5 4 8 11 15 6 1486 534 75 700 1 16 17 4 12 13 9 10 18 6 5 15 11 2 14 7 3 8 1465 553 55 701 1 17 6 14 3 12 9 10 18 15 7 13 11 4 2 5 16 8 1261 554 85 731 1 17 16 4 10 13 11 8 18 7 6 15 3 12 2 5 14 9 1480 584 78 732 2 1 18 17 3 5 13 15 8 14 9 12 4 7 16 10 6 11 749 585 92 1135 2 17 16 3 14 15 6 12 18 10 1 13 9 4 7 8 5 11 1622 769 62 1136 3 1 18 16 2 6 14 12 9 13 8 15 4 7 17 11 5 10 1149 770 94 1371 3 16 15 4 10 18 6 12 17 8 9 11 2 13 1 7 14 5 1527 829 71 1372 4 1 16 17 13 3 5 14 15 7 8 10 2 12 18 9 11 6 771 600 81 1512 4 16 11 7 2 15 14 3 17 13 5 18 9 8 1 6 12 10 421 336 92 1513 5 1 15 17 2 3 16 13 4 12 14 10 8 7 18 9 6 11 812 621 93 1585 5 15 6 12 2 11 13 3 17 14 4 18 9 8 1 7 16 10 422 337 103 1586 6 1 14 17 7 3 11 5 16 9 4 18 2 13 15 10 12 8 533 414 104 1636 6 16 5 11 2 13 12 3 17 14 4 18 10 7 1 8 15 9 350 281 100 1637 7 1 13 17 5 6 10 9 12 18 4 11 2 16 3 8 15 14 672 525 116 1645 7 13 4 14 2 12 10 5 16 15 3 18 6 9 1 11 17 8 582 449 109 1646 8 2 12 16 4 1 17 7 6 11 5 18 3 10 15 14 9 13 669 522 116 1660 8 7 9 14 3 6 15 4 11 13 5 17 1 16 2 10 18 12 604 467 123 1661 9 1 15 13 6 5 14 8 7 17 3 12 2 16 4 10 11 18 536 417 120 1671 9 8 5 16 1 7 14 4 11 17 2 18 6 10 3 12 15 13 594 459 124 1672 10 3 7 18 1 2 17 5 6 13 9 15 4 14 8 11 16 12 547 424 126 Points are #'s 1673 10 3 7 18 4 5 11 8 9 17 1 16 2 12 6 15 14 13 542 421 126 10 to 18 1674 10 4 8 16 2 5 15 7 6 14 9 13 1 17 3 11 18 12 634 492 126 here to end 1675 10 5 7 16 4 1 17 2 9 13 3 18 6 12 8 11 14 15 607 470 126 1676 10 6 5 17 8 1 12 7 9 15 2 13 4 14 3 11 18 16 671 524 126
Sol.. | -------- cell value ----- Upper case indicates the points --------| Compl Pair Point Remarks # . A b c D e f G h i J k L m N o P Q R ment # Total 1 1 3 16 18 2 6 12 17 4 5 7 10 14 8 11 15 13 9 6 1 91 2 1 3 16 18 2 6 12 17 4 5 9 8 14 10 13 11 15 7 4 2 87 3 1 3 16 18 2 6 12 17 5 4 10 8 9 15 7 11 14 13 10 3 96 4 1 3 16 18 2 6 12 17 5 4 10 8 15 9 13 11 14 7 2 2 84 5 1 3 16 18 2 7 11 17 6 4 10 8 9 14 5 13 12 15 13 4 96 6 1 3 16 18 2 8 10 17 5 6 12 4 15 11 13 9 14 7 1 1 80 7 1 3 16 18 2 8 10 17 6 5 13 4 12 14 11 7 15 9 8 5 83 8 1 3 16 18 2 8 10 17 7 4 6 12 13 5 11 15 14 9 7 5 88 9 1 3 16 18 2 11 7 17 6 8 10 4 9 14 5 13 12 15 12 6 92 10 1 3 16 18 2 12 6 17 10 5 9 8 14 4 13 11 15 7 3 3 75 11 1 3 16 18 2 12 6 17 11 4 8 10 7 9 5 13 14 15 14 7 90 12 1 3 16 18 2 14 4 17 10 7 9 6 13 5 8 15 11 12 9 6 79 13 1 3 16 18 2 14 4 17 10 7 9 6 13 5 12 11 15 8 5 4 75 14 1 3 16 18 2 14 4 17 12 5 11 6 8 10 7 9 15 13 11 7 81 15 1 3 18 16 2 8 12 17 4 5 9 6 14 10 13 11 15 7 1310 8 83 16 1 3 18 16 2 8 12 17 5 4 6 10 9 11 7 15 14 13 1318 9 96 17 1 3 18 16 2 8 12 17 5 4 6 10 13 7 11 15 14 9 1312 10 88 18 1 3 18 16 2 8 12 17 5 4 10 6 9 15 7 11 14 13 1317 11 92 19 1 3 18 16 2 8 12 17 5 4 10 6 15 9 13 11 14 7 1309 12 80 20 1 3 18 16 2 12 8 17 9 4 10 6 7 13 5 11 14 15 1320 13 88 21 1 3 18 16 2 12 8 17 9 4 10 6 15 5 13 11 14 7 1308 14 72 22 1 3 18 16 2 12 8 17 9 4 11 5 15 6 13 10 14 7 1307 15 71 23 1 3 18 16 2 14 6 17 10 5 7 8 12 4 9 15 13 11 1315 16 79 24 1 3 18 16 2 14 6 17 10 5 7 8 12 4 11 13 15 9 1313 17 77 25 1 3 18 16 2 14 6 17 10 5 8 7 13 4 9 15 12 11 1314 18 77 26 1 3 18 16 2 14 6 17 10 5 11 4 8 12 7 9 15 13 1319 19 81 27 1 3 18 16 2 14 6 17 10 5 11 4 13 7 12 9 15 8 1311 20 71 28 1 3 18 16 2 15 5 17 12 4 10 6 9 8 7 11 14 13 1316 21 78 29 1 4 15 18 2 5 13 16 6 3 9 11 12 10 14 8 17 7 40 22 88 55 1 4 18 15 3 11 9 17 10 2 13 5 16 6 8 14 7 12 1481 40 71 56 1 5 14 18 2 7 11 15 9 3 4 17 8 6 10 13 16 12 68 41 97 84 1 5 18 14 4 13 7 17 8 6 2 12 10 3 11 16 15 9 1404 60 83 85 1 6 13 18 2 3 15 14 5 4 11 10 8 17 7 9 12 16 97 61 102 153 1 6 18 13 5 16 4 17 14 3 15 2 12 8 9 7 10 11 1595 121 59 154 1 7 12 18 2 14 4 13 10 11 9 6 3 15 8 5 17 16 169 122 93 216 1 7 18 12 6 11 9 17 4 8 2 10 14 3 15 16 13 5 1348 176 77 217 1 8 11 18 2 3 15 12 5 6 7 14 17 4 16 13 10 9 233 177 90 322 1 8 18 11 4 13 10 14 9 5 12 3 15 7 6 16 2 17 1231 268 72 323 1 9 10 18 2 3 15 11 7 5 17 6 16 13 14 4 8 12 337 269 82 428 1 9 18 10 8 16 4 17 15 2 11 7 3 12 6 5 13 14 1588 357 68 429 1 10 9 18 3 2 15 11 5 7 16 6 13 17 12 4 8 14 437 358 90 531 1 10 18 9 8 15 6 16 13 3 12 5 11 7 4 14 2 17 1164 430 64 532 1 11 8 18 5 2 13 12 3 10 6 14 7 15 16 4 17 9 537 431 101 609 1 11 18 8 10 16 4 17 14 3 12 5 15 2 13 9 6 7 1675 484 45 # 1 - 9 at 610 1 12 7 18 8 2 10 14 3 11 4 16 15 5 17 13 9 6 576 458 89 the points 678 1 12 18 7 11 14 6 17 10 5 2 13 8 3 16 9 15 4 1500 533 63 679 1 13 6 18 10 2 8 15 3 12 4 16 9 11 17 7 14 5 416 345 92 770 1 13 18 6 12 16 4 17 14 3 8 9 11 2 15 7 10 5 1667 579 47 771 1 14 5 18 11 3 6 15 8 9 7 17 2 16 10 4 13 12 311 258 96 842 1 14 18 5 12 17 4 16 15 3 7 10 2 9 8 6 11 13 1627 624 62 843 1 15 4 18 13 5 2 16 3 17 6 11 10 12 14 9 8 7 103 72 85 908 1 15 18 4 14 13 7 17 8 6 2 12 10 3 11 16 5 9 1403 664 63 909 1 16 7 14 15 4 5 17 3 13 12 6 10 18 9 8 2 11 400 329 78 945 1 16 18 3 15 14 6 17 10 5 11 4 13 7 12 9 2 8 1676 691 45 # 1 - 9 at 946 2 3 16 17 1 7 13 15 4 6 11 5 18 8 12 14 10 9 956 692 84 the points 1306 2 16 15 5 17 13 3 18 9 8 1 14 4 7 12 10 11 6 1567 824 66 1307 3 1 16 18 2 6 12 17 4 5 8 9 10 13 7 14 15 11 22 15 100 1479 3 15 16 4 17 12 5 18 9 6 2 14 1 11 10 8 13 7 1571 836 71 1480 4 1 15 18 2 7 11 16 3 8 10 5 17 9 12 14 13 6 54 39 88 1539 4 16 13 5 18 7 8 17 3 10 1 14 2 15 11 9 12 6 1536 837 83 1540 5 1 14 18 3 6 11 16 2 9 8 7 10 15 4 17 12 13 83 59 107 1594 5 13 9 11 17 4 6 18 2 12 1 16 3 15 7 14 10 8 1477 834 97 1595 6 1 13 18 2 10 8 14 7 9 4 12 5 11 3 17 16 15 153 121 112 1631 6 9 10 13 14 4 7 18 5 8 3 17 1 16 2 15 11 12 1289 807 105 1632 7 2 14 15 6 9 8 16 3 11 1 12 4 13 5 17 18 10 881 646 111 1649 7 11 6 14 15 1 8 16 4 10 5 17 2 18 3 13 9 12 897 656 108 1650 8 2 12 16 6 7 9 15 3 11 1 14 4 13 5 17 18 10 883 648 116 1660 8 7 11 12 5 6 15 9 4 10 1 16 2 14 3 17 13 18 829 611 123 1661 9 3 11 15 1 4 18 8 2 10 5 12 6 16 7 13 17 14 591 466 124 1671 9 7 10 12 5 6 15 8 4 11 1 16 2 14 3 17 13 18 830 612 125 1672 10 2 9 17 1 7 13 8 5 12 3 14 6 11 4 18 15 16 894 655 126 Points are #'s 1673 10 4 6 18 2 1 17 7 3 11 5 16 9 12 8 15 14 13 735 557 126 10 to 18 1674 10 4 6 18 3 2 15 8 1 14 5 13 7 16 9 12 17 11 732 555 126 to the end 1675 10 6 5 17 4 3 14 7 1 16 2 15 9 11 8 18 12 13 609 484 126 1676 10 7 9 12 6 5 15 8 1 14 2 13 4 16 3 18 11 17 945 691 126
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September 09, 2003
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