document.write( "Question 1199424: assuming you had a unlimited supply of 3cent and 7cent stamps what is the largest amount os postage you cannot make? \n" ); document.write( "

Algebra.Com's Answer #833304 by ikleyn(52898) $\"\"$ $\"About$

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\n" ); document.write( "Assuming you had a unlimited supply of 3cent and 7cent stamps,
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document.write( "With 3-cent and 7-cent stamps, the  ANSWER  is  11 cents.\r\n" );
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document.write( "    Indeed, it is easy to check that you can not \r\n" );
document.write( "    combine 11 cents using 3c and 7c stamps, only.\r\n" );
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document.write( "    From the other side, it is easy to prove that \r\n" );
document.write( "    you can combine any number of cents greater than 11, \r\n" );
document.write( "             using 3c and 7c stamps.\r\n" );
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document.write( "Indeed, 12 = 4*3;  13 = 7 + 2*3;  14 = 2*7.\r\n" );
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document.write( "Let N be the number of cents,  N >= 12.\r\n" );
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document.write( "    (a)  If N is a multiple of 3, you simply combine N as \r\n" );
document.write( "         the integer number    of 3c stamps.\r\n" );
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document.write( "    (b)  If N >= 12 gives the remainder 1 when divided by 3, then  (N-1)  \r\n" );
document.write( "         is a multiple of 3, and you can combine N-1 cents using 3c stamps, only.\r\n" );
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document.write( "         In this combination, you will have at least four 3c stamps.\r\n" );
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document.write( "         Now from this combinations of 3c stamps, take off two 3c stamps and add \r\n" );
document.write( "         one 7c stamp - it will be your desired combination for N cents.\r\n" );
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document.write( "    (c)  If N >= 12 gives the remainder 2 when divided by 3, then  (N-2)  \r\n" );
document.write( "         is a multiple of 3, and you can combine N-2 cents using 3c stamps, only.\r\n" );
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document.write( "         In this combination, you will have at least four 3c stamps.\r\n" );
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document.write( "         Now, from this combinations, take off four 3c stamps and add \r\n" );
document.write( "         two 7c stamps - it will be your desired combination for N cents.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus I proved for you that you can combine everything above or equal 12 cents.\r
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\n" ); document.write( "\n" ); document.write( "So, 11 cents is your answer to this problem.\r
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\n" ); document.write( "\n" ); document.write( "For more general problem, see well explained solution at this link\r
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\n" ); document.write( "\n" ); document.write( "https://www.usna.edu/Users/physics/mungan/_files/documents/Scholarship/StampsProblem.pdf\r
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