Patterns /Encodings
Hexadecimal Repdigits
In base sixteen every digit is the same: 255 is FF, 4095 is FFF, and 43690 is AAAA.
How long might hexadecimal repdigits take?
1 in 16,949.2 per roll · 16,949 rolls on average.
At one daily specimen a day, the mean is about 46.4 years. A 50% chance takes 11,748 rolls; 90% takes 39,026.
7 daily rolls
1 in 2,422
30 daily rolls
1 in 565
365 daily rolls
2.13%
1 in 565 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.
With only fifteen non-zero hex digits and five usable lengths in this range, the total count stays very small — as the figure above shows.
Hex repdigits are everywhere in software even when nobody calls them that: FF is a full colour channel, FFFF a sixteen-bit maximum, and AAAA and 5555 are the alternating bit patterns used to test memory.
Because this trait depends entirely on base-sixteen notation, it sits in the representation group and is scored separately from anything the decimal digits are doing.
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.