SOLUTION: Question: Use the 20 sequences below to derive general formulae for t4 through to t12 for any other sequence in the same pattern given t1, t2 and t3. All the 20 sequences follow th

Question 1197121: Question: Use the 20 sequences below to derive general formulae for t4 through to t12 for any other sequence in the same pattern given t1, t2 and t3. All the 20 sequences follow the same pattern.
tn is defined as: 0 > tn ≤ 2048
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12
Sequence 1 1188 861 1608 205 788 370 2040 1907 411 143 276 328
Sequence 2 302 1667 615 238 51 510 2044 40 205 293 533 1337
Sequence 3 197 1725 1866 1158 1536 1905 723 1336 412 1554 1463 924
Sequence 4 101 352 262 1683 22 644 346 1843 1838 577 1946 1635
Sequence 5 424 1586 1210 1469 563 610 1424 69 173 638 574 1217
Sequence 6 1263 1030 688 748 2005 1554 430 175 417 510 1747 1482
Sequence 7 1979 156 1338 1004 1433 672 555 1451 1703 452 1171 815
Sequence 8 1179 98 1279 601 1224 446 905 549 1972 651 1161 1261
Sequence 9 1157 1326 1655 380 529 1477 537 932 509 1511 1785 893
Sequence 10 1160 1152 813 1064 1171 48 1894 322 1926 1074 1857 755
Sequence 11 1130 1746 1009 1609 752 6 713 1277 1253 479 1006 308
Sequence 12 116 1647 1944 1156 2016 2028 853 1561 1967 760 1040 1712
Sequence 13 208 699 942 1171 360 1701 327 856 330 14 1844 686
Sequence 14 886 8 1928 748 1128 246 286 502 172 1825 1083 708
Sequence 15 1719 2005 419 1613 1095 1926 828 227 1757 1485 782 1488
Sequence 16 1482 1305 1068 893 1018 1732 1328 1246 1305 617 1178 1654
Sequence 17 1529 363 786 624 1476 1242 547 1453 41 56 1285 1633
Sequence 18 1832 892 541 972 1208 1287 1208 1825 1144 1213 704 1231
Sequence 19 1772 1434 1208 1829 556 1047 1205 173 1225 391 503 1209
Sequence 20 1273 376 1431 1545 36 1869 1255 386 865 472 154 36

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

There is no way to use formal mathematics to solve this problem and know that the answer you come up with is right.

With no guidance of any sort as to what kind of sequences these are, finding a pattern that fits all of them is only a matter of playing with numbers; and any such pattern you come with might not be the "right" pattern.

Spend as much (or as little!) time as you want playing with this problem; we can't help you because a definitive solution is not possible.

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