Below are five sequences of the digits 0-9 but each have been sorted based on a single criterion.

1) $1260459378$

2) $1742350698$

3) $0152469378$

4) $5463728190$

5) $1235904687$

Name the criteria used to sort each sequence.

  • $\begingroup$ Are you saying that you have individual digits (One time each of 0, 1, 2,...) and then sorted them by a single criterium to get the sequence in 1)? And then applied the same criterion to a new set of 10 digits and got the sequence in 2)? etc. ? Or is the criterium different for each of the five? $\endgroup$ – BmyGuest Mar 16 at 12:28
  • 1
    $\begingroup$ @BmyGuest A different criterion was used for sorting each of the five. They each started out as 0123456789 before being sorted. $\endgroup$ – DenverCoder1 Mar 16 at 12:30
  • $\begingroup$ For 3) Prob wrong but, is it perhaps 01425... instead of 01524... ? $\endgroup$ – Prim3numbah Mar 16 at 13:13
  • $\begingroup$ @Prim3numbah It is correct as is. $\endgroup$ – DenverCoder1 Mar 16 at 13:14

Note 1: Number 3 was solved by hagfy in the comments.

Note 2: Where two or more digits are equal in any ordering below, the digits are sorted numerically.


Sort the digits by number of letters in the spelling.


Sort the digits by number of segments used in 7-segment display.


Sort by number of letters in the Roman numeral representation of the digit.


Sort by absolute distance from 5.
Alternatively, sort digits by number of dashes in Morse Code representation.


Sort by number of dots in braille representation of the digit.

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  • 2
    $\begingroup$ I think 3 could be rot13(gur ahzore bs punenpgref va ebzna ahzrenyf) $\endgroup$ – hagfy Mar 16 at 14:40
  • $\begingroup$ @hagfy Brilliant, that must be it! $\endgroup$ – hexomino Mar 16 at 14:41
  • $\begingroup$ All of those are correct! $\endgroup$ – DenverCoder1 Mar 16 at 14:49

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