wu :: forums « wu :: forums - ZIP Codes » Welcome, Guest. Please Login or Register. May 19th, 2024, 1:39am

RIDDLES SITE WRITE MATH! Home Help Search Members Login Register

wu :: forums    riddles    easy (Moderators: Grimbal, william wu, SMQ, towr, Eigenray, Icarus, ThudnBlunder)    ZIP Codes « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: ZIP Codes  (Read 858 times) Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 ZIP Codes   « on: Jun 16th, 2003, 12:53pm » Quote Modify In America they make use of ZIP (zoning improvement plan) codes to help direct mail. Each city/town makes use of a unique 5-digit code (we shall ignore ZIP+4 codes); for example, Aspen, Colorado is 81611.   However, due to rotational symmetry certain codes, like the one used for Aspen, Colorado, are detour-prone, as they could be read as a different code upside down. As a result, 11918 (Aspen's ZIP code read upside down) is not used.   How many 5-digit ZIP codes are detour-prone?   You may consider 81611 and 11918 as two separate detour-prone codes. However, be careful, as codes like, 66899, are not detour prone! IP Logged mathschallenge.net / projecteuler.net Leo Broukhis Senior Riddler     Gender: Posts: 459 Re: ZIP Codes   « Reply #1 on: Jun 16th, 2003, 5:24pm » Quote Modify Detour-prone ZIP codes can only consist of digits 1, 6, 8, 9, 0 (total 55). Among those, non-detour prone are codes that:   Have 1, 8, or 0 in the middle Have 11, 88, 00, 69, or 96 as the first and the last digit Have 11, 88, 00, 69, or 96 as the second and the fourth digit - total 75.     The total number of detour-prone codes is 3125 - 75 = 3050. IP Logged Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: ZIP Codes   « Reply #2 on: Jun 18th, 2003, 11:39am » Quote Modify Nice work, Leonid. Of course the obvious follow-up question is:   How many n-digit numbers are 'detour prone'? IP Logged mathschallenge.net / projecteuler.net ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: ZIP Codes   « Reply #3 on: Jun 18th, 2003, 1:44pm » Quote Modify Quote: How many n-digit numbers are 'detour prone'?   :     For n odd   N = 5n - 3*5(n-1)/2   For n even   N = 5n - 5n/2   :   A nice little puzzle, Sir Col.     « Last Edit: Jun 18th, 2003, 1:46pm by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

Powered by YaBB 1 Gold - SP 1.4!
Forum software copyright © 2000-2004 Yet another Bulletin Board