All Distinct
Every digit shows up exactly once.
A number of three or more digits with no digit repeating, like 123, 102 or 987654. Two-digit numbers don’t count — “no repeats” is too easy with only two digits.
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There are 168,480 of them, 16.8%. The count is textbook permutation: 9×9×8=648 for three digits, 4,536 for four, 27,216 for five, and 9×9×8×7×6×5=136,080 for six — shrinking degrees of freedom written into every term.
Only about 15.1% of six-digit numbers are all-distinct — over 80% of random six-digit numbers repeat somewhere. It’s the birthday paradox in digit form: with 23 people a shared birthday is more likely than not; with six slots sharing ten digits, collisions are the norm.
Together with Exactly One Pair, Two Pairs and friends it partitions the repetition spectrum: any number of 3+ digits is either all-distinct or lands in some repetition tier. 123456 and 987654 are the family’s figureheads — also Fully Ascending/Descending and Straights.