rookie1ja 13 Report post Posted March 30, 2007 5-digit Number - Back to the Number Puzzles What 5-digit number has the following property? If we put numeral 1 in front of the number, we get a number three times smaller, than if we put the numeral 1 behind this number. This old topic is locked since it was answered many times. You can check solution in the Spoiler below. Pls visit New Puzzles section to see always fresh brain teasers. 5-Digit Number - solution Using an easy equation: 3(x+100000) = 10x+1 we find out that the number is 42857. Share this post Link to post Share on other sites

Guest Report post Posted August 11, 2007 There is actually another way to solve this puzzle, figuiring out the answer digit by digit, backwards. Can someone figure out what it is? Share this post Link to post Share on other sites

Guest Report post Posted August 13, 2007 There is actually another way to solve this puzzle, figuiring out the answer digit by digit, backwards. Can someone figure out what it is? Yes, I did it this way. It is slower, but perhaps more fun. First you write the equation like a long multiplication question: 1 a b c d e x_______3 a b c d e 1 This is the logic: e x 3 ends in 1. e must be 7 (7x3=21, carry the 2) d x 3 ends in 7-2. d must be 5 (5x3=15, carry the 1) c x 3 ends in 5-1. c must be 8 (8x3=24, carry the 2) b x 3 ends in 8-2. b must be 2 (2x3=6, no carry) a x 3 ends in 2. a must be 4 (4x3=12, carry the 1) 1 x 3 ends in 4-1. this is true. ______2 1 a b c d 7 x_______3 a b c d 7 1 _____1 1 a b c 5 7 x_______3 a b c 5 7 1 ___2 1 a b 8 5 7 x_______3 a b 8 5 7 1 1 a 2 8 5 7 x_______3 a 2 8 5 7 1 1 1 4 2 8 5 7 x_______3 4 2 8 5 7 1 (carries in yellow) Share this post Link to post Share on other sites

Guest Report post Posted August 13, 2007 Great job! Share this post Link to post Share on other sites

Guest Report post Posted October 9, 2007 I solved algebraically but I had to see zAlbee's way for myself...and it works! Very clever solution Share this post Link to post Share on other sites

Guest Report post Posted December 8, 2007 The original solution doesn't work. It gives you a decimal that, when rounded, gives you the correct answer. But, if you change it to -1 it removes the decimal. Just pointing out that it needs a slight adjustment. It took me awhile and I resorted to guess and check but, thanks to my dad's idea, I used microsoft excel. Share this post Link to post Share on other sites

Guest Report post Posted December 12, 2007 The original solution doesn't work. It gives you a decimal that, when rounded, gives you the correct answer. No, try it again. The original solution works fine. 100,000 + x = (10x + 1) / 3 resolves uniquely to x = 42,857. Share this post Link to post Share on other sites

Guest Report post Posted February 12, 2008 (edited) Very cleaver guys. I tried to not use a calculator, so I made it a little harder for me. I assumed the answer was "55555" to start and did the math and it was close but not right. Then I tried "33333" and that was close and not right, but it showed me the answer was between the two. Then I tried "44444" and that was closer and then I knew the answer was between 44444 and 33333. I got into the right ballpark, but I cheated and looked at this point. At least I narrowed to 11111 possible answers. which, 11111, is consequently the only 5 digit number thats solution is exactly the same when you ad a 1 to the beginning or end. LAUGH!!! Edited February 12, 2008 by IceCreamTruck Share this post Link to post Share on other sites

Guest Report post Posted March 4, 2008 As you call it"the original solution"does work,doesn't give you any decimal just because is the correct equation.If you can't construct such a simple one by your own,at least try to do the math by puting the given number at "x" place and you'll find out,that everything is o'k.Personaly.for me is more fun to solve it digit by digit,because is to fast with the equation. Share this post Link to post Share on other sites

Guest Report post Posted March 5, 2008 .11111 the furture you go away from the point the smaller it ggets Share this post Link to post Share on other sites

Guest Report post Posted July 4, 2008 I found almost but because of my lack of understanding on question.. I thought 5 digit number including '1'. so I ended up till 28571 and 12857 If I would have tried for next number.. ie 6th I had found the answer.. Anyway misunderstanding is also a type of FAIL Share this post Link to post Share on other sites

Guest Report post Posted October 24, 2009 the five digit number is 42857, it satisfies the given condition. 1st condition: five digit number [i.e., 42857] 2nd condition: if the digit 1 is placed before the five digit number [i.e., 42857] the number is now 142857 which should be three times the number which is formed when the digit 1 is placed after the five digit number [i.e., 428571], which obviously is true. In mathematical solution, 142857= 1/3(428571) =142857 Please don't get confused, this is the correct answer. Very cleaver guys. I tried to not use a calculator, so I made it a little harder for me. I assumed the answer was "55555" to start and did the math and it was close but not right. Then I tried "33333" and that was close and not right, but it showed me the answer was between the two. Then I tried "44444" and that was closer and then I knew the answer was between 44444 and 33333. I got into the right ballpark, but I cheated and looked at this point. At least I narrowed to 11111 possible answers. which, 11111, is consequently the only 5 digit number thats solution is exactly the same when you ad a 1 to the beginning or end. LAUGH!!! Share this post Link to post Share on other sites