document.write( "Question 368581: what is the largest multiple of 12 that can be written using each 0, 1,2,3,4,5,6,7,8,9 exactly once? \n" ); document.write( "
Algebra.Com's Answer #262684 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's answer is incorrect because it does not contain a 0.\r\n" );
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document.write( "Here's my reasoning:\r\n" );
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document.write( "The largest possible integer using all ten digits once each is 9876543210\r\n" );
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document.write( "But it's not divisible by 12 because dividing that by 12 gives 823045267.5\r\n" );
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document.write( "However that tells us that the whole part of that, 823045267, times 12, is \r\n" );
document.write( "the largest multiple of 12 less than 9876543210\r\n" );
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document.write( "823045267×12 = 9876543204\r\n" );
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document.write( "Unfortunately that does not use all 10 ten digits once.  However the first\r\n" );
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document.write( "8 digits are all different.\r\n" );
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document.write( "So the problem is at least with the last two digits.\r\n" );
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document.write( "However neither 9876543210 nor 9876543201 is a multiple of 12\r\n" );
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document.write( "So the problem is at least with the last three digits \r\n" );
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document.write( "Let's check 9876543000 to see if it's divisible by 12\r\n" );
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document.write( "Yes it is because 9876543000/12 = 823045250\r\n" );
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document.write( "Now if we add any multiple of 12 to 9876543000, we will get\r\n" );
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document.write( "a multiple of 12.  Can we think of a multiple of 12 that\r\n" );
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document.write( "uses the remaining digits 0, 1, and 2.  Indeed we can! For\r\n" );
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document.write( "120 is a multiple of 12 and it uses those three digits.  No\r\n" );
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document.write( "other arrangement of those three digits is a multiple of 12.\r\n" );
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document.write( "So we add 120 to 9876543000 and get 9876543120.\r\n" );
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document.write( "That's the largest integer that uses all the digits and is also\r\n" );
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document.write( "a multiple of 12.\r\n" );
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document.write( "Answer: 9876543120\r\n" );
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document.write( "Edwin

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