egrep matching patterns containing 3 repeated digits, not consecutive - regex

Question

Use egrep to match lines containing 3 repeated digits, not necessarily consecutive,i.e "3 33", "55 5", "666" or "a6b6c6d". I have an initial thought.
I tried:
egrep '1[^1]*1[^1]*1' test
This will recoginize stuff like 1abd1df31.
However, I try not to enumerate all digit from 0 to 9. So how can I generalize this using back reference?
Thanks ahead!
NOTE that: there these three digit should be identical. ie. 3aa2aa1aa should not match.

Answer 1

This will do it:
/(?=.*?(\d))(?:(?:.*?\1){3})/
DEMO
EXPLANATION:
(?=.*?(\d))(?:(?:.*?\1){3})
Assert that the regex below can be matched, starting at this position (positive lookahead) «(?=.*?(\d))»
Match any single character that is not a line break character «.*?»
Between zero and unlimited times, as few times as possible, expanding as needed (lazy) «*?»
Match the regular expression below and capture its match into backreference number 1 «(\d)»
Match a single digit 0..9 «\d»
Match the regular expression below «(?:(?:.*?\1){3})»
Match the regular expression below «(?:.*?\1){3}»
Exactly 3 times «{3}»
Match any single character that is not a line break character «.*?»
Between zero and unlimited times, as few times as possible, expanding as needed (lazy) «*?»
Match the same text as most recently matched by capturing group number 1 «\1»

Answer 2

This works for simple cases:
egrep '^[^0-9]*([0-9])[^0-9]*\1[^0-9]*\1[^0-9]*$'
Explanation:
[^0-9]* zero or more non-digits
([0-9]) one digit captured with parens
\1 back-reference to the captured digit
[^0-9] zero or more none digits
^ and $ beginning and end of line
Caveat programmor:
It matches 3 foo 3 bar 3 but fails for 3 4 3 baz 3. In other words, no other digits are allowed in the line, just the 3 you're looking for.
Try this Perl one-liner to match the tricky cases with multiple digit types.
perl -ne '$i=$_;%a=();$a{$_}++for(split//,$i);for(0..9){if($a{$_}==3){print $i;last}}'
For each line $i it creates a hash %a addressed by each character of the line, storing occurrence counts. Then I check for digits with occurrence counts of 3, if any found, line $i is printed.