document.write( "Question 1005929: In a certain city, there are four streets going north-south and seven streets going east-west. How many street paths start at the southwest corner of the city, end at the northeast corner of the city, and have the shortest possible length? \n" ); document.write( "
Algebra.Com's Answer #622144 by AnlytcPhil(1806) $\"\"$ $\"About$
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document.write( "Suppose the grid of streets is like this:\r\n" );
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document.write( "To get from the green circle to the red circle the shortest\r\n" );
document.write( "way, we must move through 9 blocks.  We must pick 3 of those\r\n" );
document.write( "blocks the go east and the rest north.  For example, one way\r\n" );
document.write( "we can go is ENNENNNEN.  That would be the green path below:\r\n" );
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document.write( "So of the 9 blocks, we must pick 3 blocks to turn east (right),\r\n" );
document.write( "and the rest we will go north (up) so the answer is \r\n" );
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document.write( "9C3 = 84 \r\n" );
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document.write( "ways to go 9 blocks from the green circle to the red circle.\r\n" );
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document.write( "FYI, here is a computer-generated list of all 84 ways:\r\n" );
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document.write( " 1. EEENNNNNN\r\n" );
document.write( " 2. EENENNNNN\r\n" );
document.write( " 3. EENNENNNN\r\n" );
document.write( " 4. EENNNENNN\r\n" );
document.write( " 5. EENNNNENN\r\n" );
document.write( " 6. EENNNNNEN\r\n" );
document.write( " 7. EENNNNNNE\r\n" );
document.write( " 8. ENEENNNNN\r\n" );
document.write( " 9. ENENENNNN\r\n" );
document.write( "10. ENENNENNN\r\n" );
document.write( "11. ENENNNENN\r\n" );
document.write( "12. ENENNNNEN\r\n" );
document.write( "13. ENENNNNNE\r\n" );
document.write( "14. ENNEENNNN\r\n" );
document.write( "15. ENNENENNN\r\n" );
document.write( "16. ENNENNENN\r\n" );
document.write( "17. ENNENNNEN\r\n" );
document.write( "18. ENNENNNNE\r\n" );
document.write( "19. ENNNEENNN\r\n" );
document.write( "20. ENNNENENN\r\n" );
document.write( "21. ENNNENNEN\r\n" );
document.write( "22. ENNNENNNE\r\n" );
document.write( "23. ENNNNEENN\r\n" );
document.write( "24. ENNNNENEN\r\n" );
document.write( "25. ENNNNENNE\r\n" );
document.write( "26. ENNNNNEEN\r\n" );
document.write( "27. ENNNNNENE\r\n" );
document.write( "28. ENNNNNNEE\r\n" );
document.write( "29. NEEENNNNN\r\n" );
document.write( "30. NEENENNNN\r\n" );
document.write( "31. NEENNENNN\r\n" );
document.write( "32. NEENNNENN\r\n" );
document.write( "33. NEENNNNEN\r\n" );
document.write( "34. NEENNNNNE\r\n" );
document.write( "35. NENEENNNN\r\n" );
document.write( "36. NENENENNN\r\n" );
document.write( "37. NENENNENN\r\n" );
document.write( "38. NENENNNEN\r\n" );
document.write( "39. NENENNNNE\r\n" );
document.write( "40. NENNEENNN\r\n" );
document.write( "41. NENNENENN\r\n" );
document.write( "42. NENNENNEN\r\n" );
document.write( "43. NENNENNNE\r\n" );
document.write( "44. NENNNEENN\r\n" );
document.write( "45. NENNNENEN\r\n" );
document.write( "46. NENNNENNE\r\n" );
document.write( "47. NENNNNEEN\r\n" );
document.write( "48. NENNNNENE\r\n" );
document.write( "49. NENNNNNEE\r\n" );
document.write( "50. NNEEENNNN\r\n" );
document.write( "51. NNEENENNN\r\n" );
document.write( "52. NNEENNENN\r\n" );
document.write( "53. NNEENNNEN\r\n" );
document.write( "54. NNEENNNNE\r\n" );
document.write( "55. NNENEENNN\r\n" );
document.write( "56. NNENENENN\r\n" );
document.write( "57. NNENENNEN\r\n" );
document.write( "58. NNENENNNE\r\n" );
document.write( "59. NNENNEENN\r\n" );
document.write( "60. NNENNENEN\r\n" );
document.write( "61. NNENNENNE\r\n" );
document.write( "62. NNENNNEEN\r\n" );
document.write( "63. NNENNNENE\r\n" );
document.write( "64. NNENNNNEE\r\n" );
document.write( "65. NNNEEENNN\r\n" );
document.write( "66. NNNEENENN\r\n" );
document.write( "67. NNNEENNEN\r\n" );
document.write( "68. NNNEENNNE\r\n" );
document.write( "69. NNNENEENN\r\n" );
document.write( "70. NNNENENEN\r\n" );
document.write( "71. NNNENENNE\r\n" );
document.write( "72. NNNENNEEN\r\n" );
document.write( "73. NNNENNENE\r\n" );
document.write( "74. NNNENNNEE\r\n" );
document.write( "75. NNNNEEENN\r\n" );
document.write( "76. NNNNEENEN\r\n" );
document.write( "77. NNNNEENNE\r\n" );
document.write( "78. NNNNENEEN\r\n" );
document.write( "79. NNNNENENE\r\n" );
document.write( "80. NNNNENNEE\r\n" );
document.write( "81. NNNNNEEEN\r\n" );
document.write( "82. NNNNNEENE\r\n" );
document.write( "83. NNNNNENEE\r\n" );
document.write( "84. NNNNNNEEE\r\n" );
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document.write( "Edwin
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