> Actually, if you consider each finger to be a binary digit (get it?) and excluding > the thumb, there's actually 10 combinations missing.
Simply considering the binary up/down is insufficient. The digits are semi-trinary, but only in theory, and obviously not truly trinary, as you aren't crossing them.
Ignoring which fingers exactly are used in certain ones, and therefore omitting spaces, I got:
1. / 0. \ 2. // 0. \\ 3. \// 0. \\/ 4. \\// 0. \/ 5. \/// 0. /// 6. \\\/ 0. \\\
Many others are redundant, impractical, illogical, impossible, or just four fingers.
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