Patterns /Sequences
Descending Sequence Numbers
Each digit is exactly one lower than the previous: 321, 6543, 987654. The mirror image of an ascending sequence, and just as scarce.
How long might descending sequence numbers take?
1 in 38,461.6 per roll · 38,462 rolls on average.
At one daily specimen a day, the mean is about 105.3 years. A 50% chance takes 26,660 rolls; 90% takes 88,560.
7 daily rolls
1 in 5,495
30 daily rolls
1 in 1,283
365 daily rolls
1 in 106
1 in 1,283 chance of at least one match in 30 independent rolls.
Waiting times are averages, not deadlines. Previous misses do not increase the next roll’s chance. Only Daily Specimens stamp your Atlas.
Like their ascending counterparts, descending sequences are pinned by their first digit and length. The count above is correspondingly small — these are among the rarest arrangements a number can have.
Descending sequences cannot pass through zero and continue, so the longest ones must start high. That ceiling is part of why the count stays low even at six digits.
A descending sequence and an ascending one never coexist in the same number, so this trait and its counterpart are mutually exclusive by construction.
Highest-scoring examples
The best-scoring numbers of four digits or more that carry this pattern. Shorter numbers are excluded here because their length alone dominates any score ranking.
Smallest examples
The first numbers in the range that match this pattern.
Related sequences patterns
Ascending Sequence Numbers
Every digit is exactly one higher than the one before it: 123, 4567, 456789. There are only a few dozen such numbers in the entire range.
Ascending Digit Runs
A partial climb: somewhere in the number sit three or more digits each one higher than the last, as in the 456 inside 74560.
Descending Digit Runs
Three or more digits each one lower than the last, appearing anywhere in the number — the 543 inside 15432, for instance.
ABAB Pattern Numbers
Two digits taking strict turns: 5252, 8080, 393939. The pattern repeats with period two from the first digit to the last.
ABCABC Pattern Numbers
A three-digit block written twice: 146146, 707707, 989989. Every six-digit number of this form is a three-digit number multiplied by 1001.