document.write( "Question 942237: arrange the digits 0 to 9 into two five-digits numbers who sum is
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Algebra.Com's Answer #574407 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor is all wrong.  He doesn't even understand what you're\r\n" );
document.write( "to do. Here's the explanation:\r\n" );
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document.write( "

\n" ); document.write( "arrange the digits 0 to 9 into two five-digits numbers who sum is
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document.write( "What we need to realize here is that the digits farther to the left\r\n" );
document.write( "contribute the most toward the sum and the digits farther to the right\r\n" );
document.write( "contribute the least toward the sum.\r\n" );
document.write( "

\n" ); document.write( "a.The least possible sum of any arrangment
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document.write( "We start with these blanks to fill in with digits\r\n" );
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document.write( "  _ _ _ _ _\r\n" );
document.write( "+ _ _ _ _ _\r\n" );
document.write( "  _ _ _ _ _\r\n" );
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document.write( "The left-most digits contribute the most to the sum, so to make them contribute\r\n" );
document.write( "the least to the sum, choose the smallest ones to go leftmost.  The smallest\r\n" );
document.write( "possible first digits are 1 nd 2.  (Can't use 0 for a first digit!). It doesn't\r\n" );
document.write( "matter whether the 1 is the first digit of the first number and the 2 is the\r\n" );
document.write( "first digit of the second digit, or vice-versa  I'll do it this way:\r\n" );
document.write( "\r\n" );
document.write( "  1 _ _ _ _\r\n" );
document.write( "+ 2 _ _ _ _\r\n" );
document.write( "  _ _ _ _ _\r\n" );
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document.write( "The digits farthest to the left contribute the most to the sum, so to make \r\n" );
document.write( "them contribute the least, choose the two smallest possible remaining digits to \r\n" );
document.write( "go leftmost.  The smallest remaining digits are 0 and 3  It doesn't matter\r\n" );
document.write( "whether the 0 is the first digit of the first number and the 3 is the first\r\n" );
document.write( "digit of the second digit, or vice-versa.  I'll do it this way:\r\n" );
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document.write( "  1 0 _ _ _\r\n" );
document.write( "+ 2 3 _ _ _\r\n" );
document.write( "  _ _ _ _ _\r\n" );
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document.write( "The next smallest two of the remaining digits are 4 and 5, so they go next:\r\n" );
document.write( "\r\n" );
document.write( "  1 0 4 _ _\r\n" );
document.write( "+ 2 3 5 _ _\r\n" );
document.write( " _ _ _ _ _\r\n" );
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document.write( "The next smallest two of the remaining digits are 6 and 7, so they go next:\r\n" );
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document.write( "  1 0 4 6 _\r\n" );
document.write( "+ 2 3 5 7 _\r\n" );
document.write( "  _ _ _ _ _\r\n" );
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document.write( "Finally the only remaining digits are the largest two 8 and 9, so they go last,\r\n" );
document.write( "where they contribute the least amount to the sum:\r\n" );
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document.write( "  1 0 4 6 8\r\n" );
document.write( "+ 2 3 5 7 9\r\n" );
document.write( "  _ _ _ _ _\r\n" );
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document.write( "And now we add to find that smallest sum:\r\n" );
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document.write( "  1 0 4 6 8\r\n" );
document.write( "+ 2 3 5 7 9\r\n" );
document.write( "  3 4 0 4 7\r\n" );
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document.write( "Answer: 34047.   You'll get that same sum if you swap any\r\n" );
document.write( "digit of one number with the corresponding digit of the\r\n" );
document.write( "other number.\r\n" );
document.write( "

\n" ); document.write( "b.The greatest possible sum of any arragment
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document.write( "Since the digits farther to the left contribute the most, we will just\r\n" );
document.write( "reverse the process for part a, and put the biggest digits first. So we\r\n" );
document.write( "put 9 and 8 first.  We just always use the biggest two remaining digits \r\n" );
document.write( "instead of the smallest ones, and we get this:\r\n" );
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document.write( "    9 7 5 3 1\r\n" );
document.write( "  + 8 6 4 2 0\r\n" );
document.write( "  1 8 3 9 5 1\r\n" );
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document.write( "Answer: 183951\r\n" );
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document.write( "Edwin
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