## 20 June 2009

### Bob rediscovers his amazing PROOF of the 7 Bridges of Konigsberg!

Re-filched from Australian Mathematics Trust. For supplying the map and the names of the bridges, I won 2 t-shirts!

Unbelievable! Unbelievable!

I Googled "Yankee Magnetic Software" (my fictitious corporation which I invented to get Free Crap from computer companies) and some lovely gentleman had posted the QuickBasic code to my Konig7 program!

Konig7 PROVES that it is impossible to cross all 7 Bridges, each bridge only once, and return to the place you started!

I've lost this program 3 computers ago -- but now I got it again!!! Thanks Gordon Shumway!!!

===========

From: Gordon Shumway
To: All
Date: 2003-03-15 20:00:08
Subject: Seven Bridges

`DECLARE SUB FrTh ()DECLARE SUB UnFrTh ()DECLARE SUB Logiq ()DECLARE SUB Menu ()DECLARE SUB NoMenu ()DECLARE SUB Pat1 ()DECLARE SUB Pat2 ()DECLARE SUB Pat3 ()DECLARE SUB Koni ()DECLARE SUB Slp ()DECLARE SUB SlpSlo ()DECLARE SUB Brugge ()    D\$ = CHR\$(148): RRPS = 8: SHRT = .01    CLS : T100K = TIMER: FOR AA = 1 TO 100000: NEXT AA    T100K = TIMER - T100K: IF T100K < 0 THEN T100K = T100K + 86400    SCREEN 12A04: CLS : Koni: Menu: LOCATE 29, 11: PRINT "        "; : LOCATE 20, 1    PRINT "         The 7 Bridges of K"; D\$; "nigsberg": PRINT    PRINT " On Sunday strolls, citizens of K"; D\$; "nigsberg"    PRINT " tried to cross all 7 bridges, each only once,  "    PRINT " and end where they started. No one ever could. "    PRINT " But no one could prove it was impossible.      ";    LOCATE 2, 52: PRINT "           KONIG7           ";    LOCATE 3, 52: PRINT "     Copyright (c) 2002     ";    LOCATE 4, 52: PRINT "      by Robert Merkin      ";    LOCATE 6, 52: PRINT "  Yankee Magnetic Software  ";    LOCATE 7, 52: PRINT "     Northampton MA USA     ";    LOCATE 9, 53:  PRINT CHR\$(34); "Solving things you never";    LOCATE 10, 53: PRINT "even knew were problems!"; CHR\$(34);    LOCATE 12, 52: PRINT "   bobmer.javanet{at}rcn.com  ";    LOCATE 13, 52: PRINT "   http://users.rcn.com/   ";    LOCATE 14, 52: PRINT "          bobmer.javanet/  ";    LINE (400, 0)-(635, 235), 12, B    D\$ = CHR\$(148): RRPS = 8: SHRT = .01    CLS : T100K = TIMER: FOR AA = 1 TO 100000: NEXT AA    T100K = TIMER - T100K: IF T100K < t100k =" T100K" href="http://users.rcn.com/" target="new">http://users.rcn.com/   ";    LOCATE 14, 52: PRINT "          bobmer.javanet/  ";    LINE (400, 0)-(635, 235), 12, BA08: G\$ = INKEY\$: IF G\$ = "" GOTO A08              IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : END : NoMenu: DZRT = SHRT: Pat1: DZRT = 2: Slp: Koni           DZRT = SHRT: Pat2: DZRT = 2: Slp: Koni           DZRT = SHRT: Pat3:                MenuA12: G\$ = INKEY\$: IF G\$ = "" GOTO A12         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN 0: CLS : ENDLINE (400, 0)-(635, 235), 0, BF: KoniLOCATE 1, 52: PRINT "After centuries of trying,  ";LOCATE 2, 52: PRINT "some K"; CHR\$(148); "nigsbergstudents    ";LOCATE 3, 52: PRINT "wrote Leonhard Euler (1707 -";LOCATE 4, 52: PRINT "1783), Europe's greatest    ";LOCATE 5, 52: PRINT "mathematician, and asked him";LOCATE 6, 52: PRINT "to solve the puzzle of the  ";LOCATE 7, 52: PRINT "7 Bridges.                  ";LOCATE 9, 52:  PRINT "Euler's notation:";LOCATE 11, 52: PRINT "   7 Bridges      abcdefg   ";LOCATE 5, 9:   PRINT "c"; : LOCATE 5, 18:  PRINT "d";LOCATE 5, 31:  PRINT "g"; : LOCATE 14, 9:  PRINT "a";LOCATE 14, 18: PRINT "b"; : LOCATE 14, 31: PRINT "f";LOCATE 10, 25: PRINT "e";A16: G\$ = INKEY\$: IF G\$ = "" GOTO A16         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 13, 52: PRINT "   4 Land Zones   ABCD      ";LOCATE 2, 39:  PRINT " C "; : LOCATE 17, 39: PRINT " B ";LOCATE 10, 5:  PRINT " A "; : LOCATE 10, 39: PRINT " D ";A20: G\$ = INKEY\$: IF G\$ = "" GOTO A20         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : END: Brugge: LOCATE 9, 52:  PRINT "To Euler, the 4 Land Zones  ";      LOCATE 10, 52: PRINT "ABCD were more important    ";      LOCATE 11, 52: PRINT "than the 7 Bridges.         ";      LOCATE 13, 52: PRINT SPACE\$(27);A24: G\$ = INKEY\$: IF G\$ = "" GOTO A24         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 13, 52: PRINT "The Word DA means:    ";LOCATE 15, 52: PRINT "     Cross from zone D";LOCATE 16, 52: PRINT "             to zone A";A28: DZRT = SHRT: FOR XX = 29 TO 18 STEP -1CIRCLE (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 0: SlpSlo: NEXT XXDZRT = 1: Slp: XXL = (18 * RRPS)           XXR = (29 * RRPS) + 8           YYC = (18 * RRPS) + 4LINE (XXL, (YYC - 4))-(XXR, (YYC + 4)), 10, BFLINE (((21 * RRPS) - 10 + 4), (17 * RRPS))-(((26 * RRPS) + 10 + 4), (20 *: SlpSloG\$ = INKEY\$: IF G\$ = "" GOTO A28         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 13, 61: PRINT "C";LOCATE 15, 73: PRINT "C"; : LOCATE 18, 60: PRINT "byeither bridge.";A32: DZRT = SHRTFOR YY = 3 TO 15: CIRCLE (((17 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((17 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YDZRT = 1: Slp: YYH = (3 * RRPS)           YYL = (15 * RRPS) + 8           XXC = (17 * RRPS) + 4LINE ((XXC + 4), YYH)-((XXC - 4), YYL), 10, BFLINE (((17 * RRPS) - 6), (5 * RRPS))-(((17 * RRPS) + 14), (14 * RRPS)), 1: SlpDZRT = SHRTFOR YY = 3 TO 15: CIRCLE (((8 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((8 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYDZRT = .5: Slp: XXC = (8 * RRPS) + 4LINE ((XXC + 4), YYH)-((XXC - 4), YYL), 10, BFLINE (((8 * RRPS) - 6), (5 * RRPS))-(((8 * RRPS) + 14), (14 * RRPS)), 12,: SlpG\$ = INKEY\$: IF G\$ = "" GOTO A32         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDFOR LL = 1 TO 25: LOCATE LL, 52: PRINT SPACE\$(28); : NEXT LL: NoMenuLOCATE 1, 52: PRINT "A Path that crosses 7   ";LOCATE 2, 52: PRINT "bridges can be described";LOCATE 3, 52: PRINT "by an 8-letter Word.    ";LOCATE 5, 52: PRINT "ABDCABDA means:         ";LOCATE 7, 52: PRINT "         Cross from A   ";LOCATE 8, 52: PRINT "                 to B   ";DZRT = .05: CIRCLE (((17 * RRPS) + 4), ((20 * RRPS) + 4)), 3, 13PAINT (((17 * RRPS) + 4), ((20 * RRPS) + 4)), 13FOR YY = 21 TO 34: CIRCLE (((17 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((17 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSloYYY = YY: NEXT YY: FOR XX = 17 TO 30CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSloXXX = XX: NEXT XX: MenuA36: G\$ = INKEY\$: IF G\$ = "" GOTO A36: NoMenu: LOCATE 9, 52: PRINT "      then cross to D";FOR YY = 34 TO 18 STEP -1CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSloYYY = YY: NEXT YY: DZRT = .05: MenuA40: G\$ = INKEY\$: IF G\$ = "" GOTO A40: NoMenu: LOCATE 10, 52: PRINT "      then cross to C";FOR YY = 17 TO 2 STEP -1CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSloYYY = YY: NEXT YY: FOR XX = 30 TO 8 STEP -1CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSloXXX = XX: NEXT XX: DZRT = .05: MenuA48: G\$ = INKEY\$: IF G\$ = "" GOTO A48: NoMenu: LOCATE 11, 52: PRINT "      then cross to A";FOR YY = 2 TO 18: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSloYYY = YY: NEXT YY: DZRT = .05: MenuA60: G\$ = INKEY\$: IF G\$ = "" GOTO A60: NoMenu: LOCATE 12, 52: PRINT "      then cross to B ...";FOR YY = 19 TO 34: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSloYYY = YY: NEXT YY: MenuA64: G\$ = INKEY\$: IF G\$ = "" GOTO A64         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDA68: LOCATE 14, 52: PRINT "How many Path Words   ";LOCATE 15, 52: PRINT "can be spelled with   ";LOCATE 16, 52: PRINT "any combination of    ";LOCATE 17, 52: PRINT "A B C and D?          "; : WZT = 0: LogiqA72: G\$ = INKEY\$: IF G\$ = "" GOTO A72         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDA76: LOCATE 14, 52: PRINT "A Path Word can't have";LOCATE 15, 52: PRINT "AA or BB or CC or DD  ";LOCATE 16, 52: PRINT "in it. Why not? How   ";LOCATE 17, 52: PRINT "many Path Words now?  "; : WZT = 1: LogiqA80: G\$ = INKEY\$: IF G\$ = "" GOTO A80         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 14, 52: PRINT "                        ";LOCATE 15, 52: PRINT "A Path Word can't have  ";LOCATE 16, 52: PRINT "BC or CB in it. Why not?";LOCATE 17, 52: PRINT "How many Path Words now?"; : WZT = 2: LogiqA84: G\$ = INKEY\$: IF G\$ = "" GOTO A84         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 14, 52: PRINT "In a Solution Path, the ";LOCATE 15, 52: PRINT "First letter must equal ";LOCATE 16, 52: PRINT "the Last letter. Why?   ";LOCATE 17, 52: PRINT "How many Path Words now?"; : WZT = 3: LogiqA88: G\$ = INKEY\$: IF G\$ = "" GOTO A88         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 14, 52: PRINT "In a Solution Path,     ";LOCATE 15, 52: PRINT "CD or DC must occur only";LOCATE 16, 52: PRINT "once. Why? How many     ";LOCATE 17, 52: PRINT "Path Words now?         "; : WZT = 4: LogiqA92: G\$ = INKEY\$: IF G\$ = "" GOTO A92         IF G\$ = "R" OR G\$ = "r" GOTO A04         IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : ENDLOCATE 15, 52: PRINT "BD or DB"; : WZT = 5: LogiqLOCATE 26, 52: PRINT "QED! No Path exists which  ";LOCATE 27, 52: PRINT "satisfies these (and other)";LOCATE 28, 52: PRINT "Rules of the puzzle!       ";LOCATE 29, 7:  PRINT "    ";A96: G\$ = INKEY\$: IF G\$ = "X" OR G\$ = "x" THEN SCREEN0: CLS : END         IF G\$ = "R" OR G\$ = "r" GOTO A04 ELSE GOTO A96SUB BruggeSHARED RRPSLINE (((8 * RRPS) - 6), (5 * RRPS))-(((8 * RRPS) + 14), (14 * RRPS)), 12, BFLINE (((17 * RRPS) - 6), (5 * RRPS))-(((17 * RRPS) + 14), (14 * RRPS)), 12, BFLINE (((30 * RRPS) - 6), (5 * RRPS))-(((30 * RRPS) + 14), (14 * RRPS)), 12, BFLINE (((8 * RRPS) - 6), (23 * RRPS))-(((8 * RRPS) + 14), (32 * RRPS)), 12, BFLINE (((17 * RRPS) - 6), (23 * RRPS))-(((17 * RRPS) + 14), (32 * RRPS)), 12, BLINE (((30 * RRPS) - 6), (23 * RRPS))-(((30 * RRPS) + 14), (32 * RRPS)), 12, BLINE (((21 * RRPS) - 10 + 4), (17 * RRPS))-(((26 * RRPS) + 10 + 4), (20 * RRPSEND SUBSUB FrThLINE (450, 442)-(546, 468), 13, BLOCATE 29, 59: PRINT "[F]reeze";END SUBSUB KoniSHARED RRPSLINE (0, 0)-((49 * RRPS), (37 * RRPS)), 10, BF         ' greenLINE (0, (7 * RRPS))-((49 * RRPS), (12 * RRPS)), 9, BF ' Pregel highLINE (0, (25 * RRPS))-((49 * RRPS), (30 * RRPS)), 9, BF ' Pregel lowLINE (0, (7 * RRPS))-((3 * RRPS), (30 * RRPS)), 9, BF ' Pregel leftLINE ((22 * RRPS), (7 * RRPS))-((26 * RRPS), (30 * RRPS)), 9, BF ' Pregel: BruggeEND SUBSUB LogiqSHARED WZT, DZRTDZRT = .5: NoMenu: FrThPP = 0: PW\$ = "DDDDDDDD"          ' prime the pumpLOCATE (19 + WZT), 59: PRINT "0";Q08: AA = 0Q12: AA = AA + 1: IF AA = 9 GOTO Q24CC = 0: UU = ASC(MID\$(PW\$, AA, 1)) + 1: IF UU = 69 THEN UU = 65: CC = 1MID\$(PW\$, AA, 1) = CHR\$(UU): IF CC = 1 GOTO Q12'    ++++   new string complete   +++++++++++++++++++++++++Q24: IF WZT < hcd =" 0:" cc =" 1" hcd =" HCD"> 1 GOTO Q64Q26: IF WZT < hbd =" 0:" cc =" 1" hbd =" HBD"> 1 GOTO Q64Q27: IF WZT = 0 GOTO Q60IF WZT <> RIGHT\$(PW\$, 1) GOTO Q64Q28: BB = 0Q32: BB = BB + 1: IF BB = 8 GOTO Q60IF WZT = 0 GOTO Q32IF MID\$(PW\$, BB, 1) = MID\$(PW\$, (BB + 1), 1) GOTO Q64IF WZT < pp =" PP"> "DDDDDDDD" GOTO Q08LOCATE (19 + WZT), 73: PRINT "done"; : UnFrTh: MenuEND SUBSUB MenuLINE (40, 442)-(219, 468), 13, BLOCATE 29, 7: PRINT "[ ]  [R]eset  e[X]it";END SUBSUB NoMenuLINE (40, 442)-(219, 468), 0, BFEND SUBSUB Pat1SHARED RRPS'     "Another trolley always comes along." -- "McTeague"'     this bucket brigade logic is sort of strange, but it works.CIRCLE (((18 * RRPS) + 4), ((18 * RRPS) + 4)), 3, 13PAINT (((18 * RRPS) + 4), ((18 * RRPS) + 4)), 13FOR XX = 19 TO 30: CIRCLE (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 17 TO 2 STEP -1: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 29 TO 8 STEP -1: CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 3 TO 34: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 9 TO 17: CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXEND SUBSUB Pat2SHARED RRPSCIRCLE (((30 * RRPS) + 4), ((3 * RRPS) + 4)), 3, 13PAINT (((30 * RRPS) + 4), ((3 * RRPS) + 4)), 13FOR YY = 4 TO 18: CIRCLE (((30 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((30 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 29 TO 17 STEP -1: CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2,PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 19 TO 34: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 16 TO 8 STEP -1: CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 33 TO 2 STEP -1: CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 9 TO 17: CIRCLE (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((YYY * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXEND SUBSUB Pat3SHARED RRPSCIRCLE (((29 * RRPS) + 4), ((18 * RRPS) + 4)), 3, 13PAINT (((29 * RRPS) + 4), ((18 * RRPS) + 4)), 13FOR XX = 28 TO 17 STEP -1CIRCLE (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((18 * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 17 TO 2 STEP -1CIRCLE (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((XXX * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 18 TO 30CIRCLE (((XX * RRPS) + 4), ((2 * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((2 * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 3 TO 34CIRCLE (((30 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((30 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYFOR XX = 29 TO 8 STEP -1CIRCLE (((XX * RRPS) + 4), ((34 * RRPS) + 4)), 2, 0PAINT (((XX * RRPS) + 4), ((34 * RRPS) + 4)), 0: SlpSlo: XXX = XX: NEXT XXFOR YY = 33 TO 18 STEP -1CIRCLE (((8 * RRPS) + 4), ((YY * RRPS) + 4)), 2, 0PAINT (((8 * RRPS) + 4), ((YY * RRPS) + 4)), 0: SlpSlo: YYY = YY: NEXT YYEND SUBSUB SlpSHARED T100K, DZRTZZ = (100000 * DZRT) / T100K: FOR TT = 1 TO ZZ: NEXT TTEND SUBSUB SlpSloSHARED T100K, DZRTDZRTSLO = .05ZZ = (100000 * DZRTSLO) / T100K: FOR TT = 1 TO ZZ: NEXT TTEND SUBSUB UnFrThLINE (450, 442)-(546, 468), 0, BFEND SUB--- Peach v1.69* Origin: Rockford Files * (248)398-6601 * (1:120/483)SEEN-BY: 633/267 270@PATH: 120/483 481 228 261/38 123/500 106/2000 633/267`

Paul P said...

I tried to read all of this post but I got a headache.

Sunday, 21 June, 2009
Vleeptron Dude said...

okay, now go to the next later post:

http://vleeptronz.blogspot.com/2009/06/yankee-magnetic-software-solving-things.html

Sunday, 21 June, 2009
site said...

This can't have effect in reality, that's what I think.

Sunday, 22 July, 2012
sex shop said...

Thanks for your post, very useful information.

Wednesday, 16 January, 2013