For openings, I think I had two of the worst ones on this thread as far as matching the number of characters for the 17,723 possibilities.
Here is a simple command-line analysis of the number of characters matching for the openings I've seen.
It doesn't correct for repeat characters and doesn't adjust for a match in the right position (see my post on page 5 to optimize positioning).
Substitute (p for +, m for -, t for *, d for /, e for =) to not have to deal with special characters.
[OPENING] [Matches at least 1 character] [Matches 2] [Matches 3] ... [Matches 8]
Previous openings listed on this thread:
7t8p9e65 17723 17561 16494 13372 7856 3221 708 86
9t8m7e65 17723 17589 16625 13583 8137 3490 791 99
3t14d7e6 17723 17675 16915 14427 9513 4158 1060 94
9t8d6e12 17723 17671 17001 14468 9286 4212 1184 218
27p38e65 17723 17679 17245 14906 10265 4997 1425 150
103m98e5 17723 17654 16857 14572 10011 4894 1435 173
60m13e47 17723 17677 17134 15163 10377 4940 1448 240
23p45e68 17723 17669 17258 15312 10870 5484 1672 181
18p45e63 17723 17682 17344 15795 11827 6220 1957 285
18p27e45 17723 17658 17320 15958 12128 6342 2035 262
12p35e47 17723 17705 17406 16004 12317 6710 2247 353
12p36e48 17723 17711 17372 15986 12339 7158 2306 334
Best for matching 8:
12d6t4e8, 12d8t4e6, 12t4d6e8, 12t4d8e6, 16d4t2e8, 16d8t2e4, 16t2d4e8, 16t2d8e4, 2d4t16e8, 2d8t16e4, 2t16d4e8, 2t16d8e4, 4d16t8e2, 4d2t8e16, 4d6t12e8, 4d8t12e6, 4t12d6e8, 4t12d8e6, 4t8d16e2, 4t8d2e16, 6d12t8e4, 6d4t8e12, 6t8d12e4, 6t8d4e12, 8d12t6e4, 8d16t4e2, 8d2t4e16, 8d4t6e12, 8t4d16e2, 8t4d2e16, 8t6d12e4,
8t6d4e12 17723 17705 17008 14530 9569 4968 1721 370
Best for matching 6 or 7:
48m12e36, 48m16e32, 48m32e16, 48m36e12, 84m21e63, 84m23e61, 84m61e23,
84m63e21 17723 17713 17459 16188 12661 7438 2429 334
Best for matching 5:
43m15e28, 43m18e25, 43m25e18, 43m28e15, 52m14e38, 52m18e34, 52m34e18,
52m38e14 17723 17705 17537 16351 12987 7007 2299 328
Best for matching 4:
45m16e29, 45m19e26, 45m26e19,
45m29e16 17723 17721 17519 16357 12365 6812 2132 285