document.write( "Question 1200281: Find the number of paths from A to B, moving up and right
\n" ); document.write( "only. Notice that two lines have been left out.\r
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\n" ); document.write( "\n" ); document.write( "https://ibb.co/3c2Fk1X \n" ); document.write( "

Algebra.Com's Answer #834379 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "This problem could probably be solved using formal mathematics with combinatorics, by finding the total number of paths from A to B without the missing lines and subtracting the number of paths that would use either or both of the missing lines.

\n" ); document.write( "But probably an easier method, since the diagram is relatively small, is the brute force method of counting the number of possible paths to each point on the grid.

\n" ); document.write( "The diagrams below show the process, leading to the final answer.

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document.write( "   1 --- X --- X --- X --- X --- X --- X --- X --- X --- X\r\n" );
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document.write( "   1 --- X --- X --- X --- X --- X     X --- X --- X --- X\r\n" );
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document.write( "   1 --- X --- X --- X --- X --- X --- X --- X --- X --- X\r\n" );
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document.write( "   1 --- X --- X --- X --- X --- X --- X --- X --- X --- X\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1\r\n" );
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document.write( "   1 --- 5 --- X --- X --- X --- X --- X --- X --- X --- X\r\n" );
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document.write( "   1 --- 4 --- X --- X --- X --- X     X --- X --- X --- X\r\n" );
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document.write( "   1 --- 3 --- X --- X --- X --- X --- X --- X --- X --- X\r\n" );
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document.write( "   1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9 ---10\r\n" );
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document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1\r\n" );
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document.write( "   1 --- 5 ---12 --- X --- X --- X --- X --- X --- X --- X\r\n" );
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document.write( "   1 --- 4 --- 7 --- X --- X --- X     X --- X --- X --- X\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 3 --- 3 --- 7 ---12 ---18 ---25 ---33 ---42 ---52\r\n" );
document.write( "   |     |           |     |     |     |     |     |     |\r\n" );
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document.write( "   1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9 ---10\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1\r\n" );
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document.write( "   1 --- 5 ---12 --- X --- X --- X --- X --- X --- X --- X\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 4 --- 7 ---14 ---26 ---44    25 ---58 ---100 --152\r\n" );
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document.write( "   1 --- 3 --- 3 --- 7 ---12 ---18 ---25 ---33 ---42 ---52\r\n" );
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document.write( "   1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9 ---10\r\n" );
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document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1\r\n" );
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document.write( "   1 --- 5 ---12 ---26 ---52 ---96 ---121---179---279---431\r\n" );
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document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 4 --- 7 ---14 ---26 ---44    25 ---58 ---100 --152\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   |     |     |     |     |     |     |     |     |     |\r\n" );
document.write( "   1 --- 3 --- 3 --- 7 ---12 ---18 ---25 ---33 ---42 ---52\r\n" );
document.write( "   |     |           |     |     |     |     |     |     |\r\n" );
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document.write( "   1 --- 2 --- 3 --- 4 --- 5 --- 6 --- 7 --- 8 --- 9 ---10\r\n" );
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document.write( "   1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1 --- 1

\n" ); document.write( "ANSWER: (If I didn't make any errors) 431
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