Saturday, June 07, 2008

Guess this Social Security Number

A certain Social Security Number has the following qualities:
  • It uses each of the digits 1 to 9 exactly once (with no zero).
  • The digits from 1 to 2 (inclusive) add up to 12.
  • The digits from 2 to 3 (inclusive) add up to 23.
  • The digits from 3 to 4 (inclusive) add up to 34.
  • The digits from 4 to 5 (inclusive) add up to 45.
  • The digit 3 is NOT next to a dash (XXX-XX-XXXX).
What is this unique Social Security Number?
at

8 comments:

  1. Joe WSun Jun 08, 11:31:00 AM PDT

    The answer is the product of the following primes:

    3 x 3 x 3 x 5 x 3503099

    ReplyDelete
  2. Don HodunMon Jun 09, 12:36:00 PM PDT

    Blaine, I assume that when you talk about the digits from 4 to 5 inclusive, a number like xyz54abcd encompasses all of the digits, i.e., you count from L to R only??

    ReplyDelete
  3. EricTue Jun 10, 05:27:00 PM PDT

    Don, under your interpretation is the solution unique?

    ReplyDelete
  4. BlaineWed Jun 11, 04:02:00 PM PDT

    Don, consider 1 and 2 the end points of a sequence of digits (e.g. 2451). That sequence adds up to 12. If you can arrange all 9 digits to meet the criteria, you've found the number.

    ReplyDelete
  5. Don HodunThu Jun 12, 05:14:00 AM PDT

    Blaine, I guess that helps. By your problem definition, 4 and 5 are the end places of the SSN in question, as all 9 digits add up to 45. I found a sequence that fit 3 of the 4 criteria, but did not limit the placement of 4 and 5 as your reply did.

    ReplyDelete
  6. Don HodunThu Jun 12, 05:21:00 AM PDT

    Here goes:

    If I pick 4 as the first digit and 5 as the last digit:

    4xx-xx-xxx5

    4xx-xx-x365 fits the 34 clue

    472-91-8365 then fits the remainder clues.

    ReplyDelete
  7. BlaineThu Jun 12, 07:46:00 AM PDT

    You got it! My logic was similar:

    As you noted, 1+2+3+...+7+8+9 = 45, so the 4 and the 5 will have to be at the ends with a total of 36 between them, though at this point order could go either way. I'll use: 4 {36} 5

    The numbers between 4 and 3 will add up to 34, which means 27 between them. What is left is 6.
    4 {27} 3 {6} 5

    The 2 must go closer to 4 in order for the sum of 23 to work. That puts 18 between them with 7 on the other side of 2.

    4 {7} 2 {18} 3 {6} 5

    And the 1 must go closer to the 3 for its sum to work: That puts 9 to the left and 8 to the right.
    4 {7} 2 {9} 1 {8} 3 {6} 5

    Technically there are two possible answers (472-91-8365 or 653-81-9279) but the puzzle also said that 3 is not adjacent to a dash so that eliminates the second answer.

    Answer:
    472-91-8365

    ReplyDelete
  8. BlaineThu Jun 12, 07:52:00 AM PDT

    Typo on the second answer:
    ^563-81-9274

    ReplyDelete

For NPR puzzle posts, don't post the answer or any hints that could lead to the answer before the deadline (usually Thursday at 3pm ET). If you know the answer, submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't assist with solving. You can openly discuss your hints and the answer after the deadline. Thank you.