document.write( "Question 714806: Find a natural number for which if we move the first digit to the last place, the number that will emerge will be half of the original.\r
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document.write( "ex 321 goes to 213 but no a sollution \n" );
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Algebra.Com's Answer #439163 by KMST(5328)![]() ![]() You can put this solution on YOUR website! Two solutions shown here. I believe there is an infinite number, but I don't know how to prove it yet. \n" ); document.write( "105,263,157,894,736,842 turns into 052,631,578,947,368,421 when you move the first digit to the end. \n" ); document.write( "(No one said that the second digit could not be zero). \n" ); document.write( "210,526,315,789,473,684 turns into 105,263,157,894,736,842 \n" ); document.write( " \n" ); document.write( "HOW I FOUND SOLUTIONS: \n" ); document.write( "Let \n" ); document.write( "The number will be \n" ); document.write( "Moving the first digit to the end yields the number \n" ); document.write( " \n" ); document.write( "Obviously, \n" ); document.write( "so \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "Computer and calculator did not help, so I took paper and pencil. \n" ); document.write( "I started dividing 1 divided by 19. \n" ); document.write( "I knew it would be a repeating decimal, and I only needed to get to the 18th digit. \n" ); document.write( "I was looking for a remainder of 2. \n" ); document.write( "I got to \n" ); document.write( " \n" ); document.write( "Multiplying it all by \n" ); document.write( " \n" ); document.write( "which means \n" ); document.write( "So I found my \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "The solutions shown above come from \n" ); document.write( " \n" ); document.write( " |