1. Forum
  2. Usenet
  3. REC.PUZZLES

  • US Chain Letters

    From leflynn@21:1/5 to All on Sun Jun 22 20:56:28 2025
    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-states-and-territories

    L. Flynn

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From user4055@newsgrouper.org.invalid@21:1/5 to All on Fri Jun 27 19:15:16 2025
    XPost: sci.lang, alt.usage.english

    leflynn <leflynn@hotmail.com> posted:

    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-states-and-territories

    L. Flynn


    _______________________

    I'd like to know the answres to these questions, esp.
    the first TWO.


    the five (5) US Territories ====== (I only knew 2 of these)


    the three (3) US Possessions ====== (I didn't know any of these)


    ___________

    Neither the Marshall Islands nor the "Truck islands" (more accurately, Truk Islands, now known as Chuuk) are U.S. territories today.

    -- Marshall Islands: Not a U.S. territory, but do host major U.S. military bases under international agreement.

    -- Truk/Chuuk Islands: Not a U.S. territory and do not currently host U.S. military bases.

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From IlanMayer@21:1/5 to leflynn on Sat Jun 28 21:19:34 2025
    On Mon, 23 Jun 2025 0:56:28 +0000, leflynn wrote:

    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-states-and-territories

    L. Flynn

    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER

    50 states (length 22):

    MI
    IN
    NV
    VT
    TN
    NM
    MN
    NC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IA
    AR
    RI
    ID
    DE

    50 states + DC + 5 territories (length 27):

    MN
    NV
    VI
    ID
    DC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PA
    AR
    RI
    IA
    AS
    SD
    DE

    50 states + DC + 5 territories + 3 possessions (length 30):

    FM
    MN
    NV
    VA
    AL
    LA
    AK
    KS
    SC
    CA
    AR
    RI
    ID
    DC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PW
    WV
    VI
    IA
    AS
    SD
    DE

    Please reply to ilanlmayer at gmail dot com

    __/\__
    \ /
    __/\\ //\__ Ilan Mayer
    \ /
    /__ __\ Toronto, Canada
    /__ __\
    ||

    --

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From HenHanna@21:1/5 to IlanMayer on Mon Jun 30 17:37:58 2025
    On Sat, 28 Jun 2025 21:19:34 +0000, IlanMayer wrote:

    On Mon, 23 Jun 2025 0:56:28 +0000, leflynn wrote:

    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-states-and-territories

    L. Flynn

    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER

    50 states (length 22):

    MI
    IN
    NV
    VT
    TN
    NM
    MN
    NC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IA
    AR
    RI
    ID
    DE

    50 states + DC + 5 territories (length 27):

    MN
    NV
    VI
    ID
    DC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PA
    AR
    RI
    IA
    AS
    SD
    DE

    50 states + DC + 5 territories + 3 possessions (length 30):

    FM
    MN
    NV
    VA
    AL
    LA
    AK
    KS
    SC
    CA
    AR
    RI
    ID
    DC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PW
    WV
    VI
    IA
    AS
    SD
    DE

    Please reply to ilanlmayer at gmail dot com

    __/\__
    \ /
    __/\\ //\__ Ilan Mayer
    \ /
    /__ __\ Toronto, Canada
    /__ __\
    ||

    --



    great... Are these the Longest chains?

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From IlanMayer@21:1/5 to HenHanna on Wed Jul 2 00:24:47 2025
    On Mon, 30 Jun 2025 17:37:58 +0000, HenHanna wrote:

    On Sat, 28 Jun 2025 21:19:34 +0000, IlanMayer wrote:

    On Mon, 23 Jun 2025 0:56:28 +0000, leflynn wrote:

    Recently Games Magazine had a Wild Card entry where the goal was to find >>> the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-states-and-territories

    L. Flynn

    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER
    SPOILER

    50 states (length 22):

    MI
    IN
    NV
    VT
    TN
    NM
    MN
    NC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IA
    AR
    RI
    ID
    DE

    50 states + DC + 5 territories (length 27):

    MN
    NV
    VI
    ID
    DC
    CA
    AL
    LA
    AK
    KS
    SC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PA
    AR
    RI
    IA
    AS
    SD
    DE

    50 states + DC + 5 territories + 3 possessions (length 30):

    FM
    MN
    NV
    VA
    AL
    LA
    AK
    KS
    SC
    CA
    AR
    RI
    ID
    DC
    CO
    OH
    HI
    IN
    NC
    CT
    TN
    NM
    MP
    PW
    WV
    VI
    IA
    AS
    SD
    DE

    Please reply to ilanlmayer at gmail dot com

    __/\__
    \ /
    __/\\ //\__ Ilan Mayer
    \ /
    /__ __\ Toronto, Canada
    /__ __\
    ||

    --



    great... Are these the Longest chains?

    They should be - found by computer

    --

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Entwistle@21:1/5 to All on Wed Jul 2 13:19:46 2025
    On Sat, 28 Jun 2025 21:19:34 +0000, IlanMayer wrote:

    SPOILER
    POILER
    OILER
    ILER
    LER
    ER
    R

    I'm a bit unsure of the categorizations for question 2, but for 3...

    50 states + DC + 5 territories + 3 possessions (length 30):

    Good job. I think there are variations on the sequence, but I can't find anything longer. The variation is just swapping the order of some blocks.

    FM, MN, NV, VA, AL, LA, AK, KS, SC, CA, AR, RI, ID, DC, CO, OH, HI, IN,
    NC, CT, TN, NM, MP, PW, WV, VI, IA, AS, SD, DE

    FM, MN, NV, VA, AL, LA, AK, KS, SC, CA, AS, SD, DC, CO, OH, HI, IN, NC,
    CT, TN, NM, MP, PW, WV, VI, IA, AR, RI, ID, DE


    --
    David Entwistle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Entwistle@21:1/5 to David Entwistle on Wed Jul 2 17:04:31 2025
    On Wed, 2 Jul 2025 13:19:46 -0000 (UTC), David Entwistle wrote:

    Good job. I think there are variations on the sequence, but I can't find anything longer. The variation is just swapping the order of some
    blocks.

    Lots of options:

    FM, MN, NV, VA, AL, LA, AK, KS, SC, CA, AR, RI, ID, DC, CO, OH, HI, IN,
    NC, CT, TN, NM, MP, PW, WV, VI, IA, AS, SD, DE
    FM, MN, NV, VA, AL, LA, AK, KS, SC, CA, AS, SD, DC, CO, OH, HI, IN, NC,
    CT, TN, NM, MP, PW, WV, VI, IA, AR, RI, ID, DE
    FM, MN, NV, VA, AL, LA, AK, KS, SC, CA, AS, SD, DC, CO, OH, HI, IN, NC,
    CT, TN, NM, MP, PW, WV, VI, IA, AR, RI, ID, DE
    FM, MN, NC, CA, AR, RI, IN, NM, MP, PW, WV, VA, AL, LA, AS, SC, CT, TN,
    NV, VI, ID, DC, CO, OH, HI, IA, AK, KS, SD, DE
    FM, MP, PW, WV, VA, AS, SC, CT, TN, NV, VI, ID, DC, CA, AR, RI, IN, NM,
    MN, NC, CO, OH, HI, IA, AL, LA, AK, KS, SD, DE
    FM, MP, PW, WV, VA, AL, LA, AK, KS, SC, CT, TN, NC, CA, AS, SD, DC, CO,
    OH, HI, IA, AR, RI, IN, NM, MN, NV, VI, ID, DE
    FM, MP, PW, WV, VA, AS, SC, CO, OH, HI, IN, NV, VI, IA, AK, KS, SD, DC,
    CT, TN, NM, MN, NC, CA, AL, LA, AR, RI, ID, DE
    FM, MN, NM, MP, PW, WV, VA, AK, KS, SD, DC, CA, AL, LA, AS, SC, CO, OH,
    HI, IN, NC, CT, TN, NV, VI, IA, AR, RI, ID, DE
    FM, MP, PW, WV, VI, IA, AR, RI, IN, NV, VA, AL, LA, AK, KS, SC, CT, TN,
    NM, MN, NC, CO, OH, HI, ID, DC, CA, AS, SD, DE
    FM, MP, PW, WV, VA, AR, RI, IA, AS, SC, CT, TN, NC, CA, AL, LA, AK, KS,
    SD, DC, CO, OH, HI, IN, NM, MN, NV, VI, ID, DE
    FM, MN, NM, MP, PW, WV, VA, AR, RI, ID, DC, CT, TN, NC, CO, OH, HI, IN,
    NV, VI, IA, AS, SC, CA, AL, LA, AK, KS, SD, DE
    FM, MP, PW, WV, VI, ID, DC, CA, AK, KS, SC, CT, TN, NV, VA, AR, RI, IN,
    NM, MN, NC, CO, OH, HI, IA, AL, LA, AS, SD, DE
    FM, MN, NM, MP, PW, WV, VI, IN, NC, CT, TN, NV, VA, AS, SD, DC, CA, AL,
    LA, AR, RI, IA, AK, KS, SC, CO, OH, HI, ID, DE
    FM, MN, NV, VI, IN, NC, CA, AS, SC, CO, OH, HI, IA, AL, LA, AR, RI, ID,
    DC, CT, TN, NM, MP, PW, WV, VA, AK, KS, SD, DE



    --
    David Entwistle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Entwistle@21:1/5 to leflynn on Thu Jul 3 07:46:44 2025
    On Sun, 22 Jun 2025 20:56:28 -0400, leflynn wrote:

    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-
    states-and-territories

    L. Flynn

    Nice problem.

    Does anyone have a strategy, other than getting a machine to do all the
    hard work, to approach this problem?

    Shuffling cards didn't get me near an optimal solution - not in the time i allowed. A matrix showing first letters across, and second letters down,
    with a mark where the zip code is valid, seems useful, but didn't lead to
    an obvious solution.

    I'm happy for a machine to do some of the work, but I'd be happier if the approach was something other than "blindly" trying every avenue and
    keeping the best solution.

    Some thoughts... It would seem sensible to consider "nodes" which only
    have one route between them first and try and include those in any
    solution. The letter matrix idea reminds me of a electronic switching
    matrix. For some reason Kirchoff and his current and voltage laws keeps
    coming to mind.


    --
    David Entwistle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From leflynn@21:1/5 to David Entwistle on Thu Jul 3 16:10:48 2025
    I'm leaving off spoiler space as Ilan has posted good solutions.

    The original problem was somewhat tractable without a computer as
    one could some eliminate states or see that they could only be the first
    or last member of the chain. There are some other ideas that reduce
    the dimension search space, similar to your node idea.

    For the full 59 pair problem, it needs a computer.
    That said, it is interesting to me that there are 9984=256*3*13
    different variations but they all use the same 30 choices.
    E.g., FMMPPWWVVIIAASSDDCCTTNNCCOOHHIINNMMNNVVAAKKSSCCAALLAARRIIDDE

    L. Flynn

    On 7/3/2025 3:46 AM, David Entwistle wrote:
    On Sun, 22 Jun 2025 20:56:28 -0400, leflynn wrote:

    Recently Games Magazine had a Wild Card entry where the goal was to find
    the longest chain of US States where the last letter of an entry in the
    chain had to be the same as the first letter of the next entry.

    Here are three more challenging problems.
    1. Find the longest chain using the two-letter US Post office codes for
    the 50 states.
    2. Same as 1. but add the postal codes for the District of Columbia and
    the five US Territories for a total of 56 two-letter codes.
    3. Same as 2. but add the postal codes for the three Possessions.

    https://faq.usps.com/s/article/What-are-the-USPS-abbreviations-for-U-S-
    states-and-territories

    L. Flynn

    Nice problem.

    Does anyone have a strategy, other than getting a machine to do all the
    hard work, to approach this problem?

    Shuffling cards didn't get me near an optimal solution - not in the time i allowed. A matrix showing first letters across, and second letters down,
    with a mark where the zip code is valid, seems useful, but didn't lead to
    an obvious solution.

    I'm happy for a machine to do some of the work, but I'd be happier if the approach was something other than "blindly" trying every avenue and
    keeping the best solution.

    Some thoughts... It would seem sensible to consider "nodes" which only
    have one route between them first and try and include those in any
    solution. The letter matrix idea reminds me of a electronic switching
    matrix. For some reason Kirchoff and his current and voltage laws keeps coming to mind.



    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Entwistle@21:1/5 to David Entwistle on Thu Jul 3 07:50:56 2025
    On Thu, 3 Jul 2025 07:46:44 -0000 (UTC), David Entwistle wrote:

    Some thoughts... It would seem sensible to consider "nodes" which only
    have one route between them first and try and include those in any
    solution. The letter matrix idea reminds me of a electronic switching
    matrix. For some reason Kirchoff and his current and voltage laws keeps coming to mind.

    Apologies to Mr Kirchhoff for getting his name wrong.

    --
    David Entwistle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From David Entwistle@21:1/5 to leflynn on Fri Jul 4 08:44:39 2025
    On Thu, 3 Jul 2025 16:10:48 -0400, leflynn wrote:

    For the full 59 pair problem, it needs a computer.
    That said, it is interesting to me that there are 9984=256*3*13
    different variations but they all use the same 30 choices.
    E.g., FMMPPWWVVIIAASSDDCCTTNNCCOOHHIINNMMNNVVAAKKSSCCAALLAARRIIDDE

    Yes, curious.

    Given a fixed starting point, it will be possible to derive the number of possible routes from the number of branches at each node along the way.
    It's going to get complicated, but it'll be standard theory for some
    branch of mathematics.

    1st step, 2 choices:

    FM, MN
    FM, MP

    2nd step, 3 choices:

    FM, MN, NC
    FM, MN, NV
    FM, MP, PW

    3rd step, 6 choices:

    FM, MN, NC, CA
    FM, MN, NC, CO
    FM, MN, NC, CT
    FM, MN, NV, VA
    FM, MN, NV, VI
    FM, MP, PW, WV

    3rd step, 15 choices:

    FM, MN, NC, CA, AK
    FM, MN, NC, CA, AL
    FM, MN, NC, CA, AR
    FM, MN, NC, CA, AS
    FM, MN, NC, CO, OH
    FM, MN, NC, CT, TN
    FM, MN, NV, VA, AK
    FM, MN, NV, VA, AL
    FM, MN, NV, VA, AR
    FM, MN, NV, VA, AS
    FM, MN, NV, VI, IA
    FM, MN, NV, VI, ID
    FM, MN, NV, VI, IN
    FM, MP, PW, WV, VA
    FM, MP, PW, WV, VI

    --
    David Entwistle

    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)