document.write( "Question 441367: Place numbers 1 through 12 randomly around a circle. Show it is impossible for all sets of three consecutive numbers to sum to 19 or 20. \n" ); document.write( "
Algebra.Com's Answer #304676 by richard1234(7193)\"\" \"About 
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Suppose that, in clockwise order, are the twelve numbers satisfying .\r
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\n" ); document.write( "\n" ); document.write( "Without loss of generality, let . It follows that , because if it equaled 19, then . This implies .\r
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\n" ); document.write( "\n" ); document.write( "Hence, , because if it was 20, then , so . By a simple inductive argument,\r
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\n" ); document.write( "\n" ); document.write( "This implies contradiction, so it cannot occur.\r
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