rookie1ja 13 Report post Posted March 30, 2007 9-digit Number - Back to the Number Puzzles Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24. 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. 9-Digit Number - solution 473816952 – if rounding changes the next numeral character Share this post Link to post Share on other sites

Guest Report post Posted July 2, 2007 I dont think my head can go that far. im Guessing the number 123456789 Share this post Link to post Share on other sites

Guest Report post Posted July 11, 2007 your solution does not make sense based on the criteria you gave. Could you explain how you came up with your solution please. in your number, you did not alternate rounding up and down and you rounded the last number which in your directions you said not to do and after your fourth time rounding, the remaining numbers add up to 23 not 24. I hope you can explain your solution, because I am very confused at this point as i had a very different solution. thank you Share this post Link to post Share on other sites

Guest Report post Posted July 11, 2007 the numbers work 473816952 you still round up for the first one, down for the second one, up for the third one and so on, then the numbers add up to 24 and it works 2 rounds down to zero, 5 stays the same 5 rounds up to zero, 9 adds one becomes 0 0 rounds down zero, 6 stays a six 6 rounds up to zero, 1 adds one becomes 2 2+8+3+7+4 =24 finish rounding numbers and you end up with 500000000 Share this post Link to post Share on other sites

Guest Report post Posted August 11, 2007 I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem: 518372946 Adam Share this post Link to post Share on other sites

Guest Report post Posted August 21, 2007 Is there any other way to do this besides trial and error? Share this post Link to post Share on other sites

Guest Report post Posted August 21, 2007 [I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem: 518372946 Adam Adam, yours does not alternate. follow: 5183729846 -- round up 5183729850 -- round up again! 5183729900 -- and we round up again...and so forth. I think you probably just missed that 4 going up to a 5 since it would alternate other than that! Share this post Link to post Share on other sites

Guest Report post Posted September 22, 2007 Adam: I came up with another answer. The problem says "The rounding alternates (up, down, up ...)" so I started rounding up, not down first. Here is what I came up with, I believe it meets all the criteria of the problem: 518372946 Perhaps Adam begins on the incorrect end. Instructions indicate one is to begin with the units, then 10's and so-on. Otherwise, he would be correct. Share this post Link to post Share on other sites

Guest Report post Posted September 26, 2007 your solution does not make sense based on the criteria you gave. Could you explain how you came up with your solution please. in your number, you did not alternate rounding up and down and you rounded the last number which in your directions you said not to do and after your fourth time rounding, the remaining numbers add up to 23 not 24. I hope you can explain your solution, because I am very confused at this point as i had a very different solution. thank you You make one mistake here: after the forth rounding (up), the 1 would have become a 2, and the sum of the remaining numbers would then INDEED be 24! This was an easy onion to peel. BoilingOil Share this post Link to post Share on other sites

Guest Report post Posted December 3, 2007 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn):546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz Share this post Link to post Share on other sites

rookie1ja 13 Report post Posted December 4, 2007 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn):546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz as already mentioned above by savagegamer90 and Boiling Oil ... the sum of the remaining numerals after 4 round-offs is indeed 24 after 1st rounding - 473816950 after 2nd rounding - 473817000 after 3rd rounding - 473817000 after 4th rounding - 473820000 so 4+7+3+8+2=24 Share this post Link to post Share on other sites

Guest Report post Posted January 18, 2008 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn):546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz your answer isn't right because your number isn't commensurable by 6 or 7 ( i had to look it up, from what I read commensurable basically means divisible by) so the number was supposed to be divisible by 6 and 7, which the original answer is Share this post Link to post Share on other sites

Guest Report post Posted February 3, 2008 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn):546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz u r incorrect. 550000000 rounds to 600000000 Share this post Link to post Share on other sites

Guest Report post Posted February 3, 2008 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn):546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz u r incorrect. 550000000 rounds to 600000000 Share this post Link to post Share on other sites

Guest Report post Posted February 15, 2008 My solution: 542673198 Chk it! divisible by 6 & 8.. round off till end n u will get 500000000 also last 5 digits will add to 24 in the process... Share this post Link to post Share on other sites

rookie1ja 13 Report post Posted February 15, 2008 My solution: 542673198 Chk it! divisible by 6 & 8.. round off till end n u will get 500000000 also last 5 digits will add to 24 in the process... 542673198 is not divisible by 7 (as the puzzle requested) Share this post Link to post Share on other sites

Guest Report post Posted February 22, 2008 (edited) This is unsolveable. Round to what? The nearest multiple of 10? The nearest multiple of 5? The nearest multiple of 2? Edited February 22, 2008 by sunshipballoons Share this post Link to post Share on other sites

rookie1ja 13 Report post Posted February 22, 2008 This is unsolveable. Round to what? The nearest multiple of 10? The nearest multiple of 5? The nearest multiple of 2? round to insanity Share this post Link to post Share on other sites

Guest Report post Posted February 13, 2010 Since you have an error in your conditions (the sum of the remaining numerals after 4 round-offs in your answer is NOT 24 as you stipulate--yours is 23) and with only 8 round-offs starting with rounding up, the last round-off has to be down, your answer is incorrect. I believe my answer is, therefore, equally valid. My 9-digit number is: 546372819 First rounding (up) yields: 546372820 2nd rounding (dn) yields: 546372800 3rd rounding (up) yields: 546373000 4th rounding (dn): 546370000 5th rounding (up): 546400000 6th rounding (dn): 546000000 7th rounding (up): 550000000 8th rounding (dn): 500000000 Thanks for the challenge. Linda, the Puzzlerz The initial answer did look correct to me (I think the description of alternate rounding, wasn't meant to say it HAS to round up first, rather it was a specifc example presented to illustrate what was meant by alternate rounding). There are a few issues with the alternative solution you presented: Your sum after 4 rounds of rounding equals 25 Also, your final round down, should have been a round up (given that the 5 dictates a round-up) Last but not least, your intial number is not divisible by 7 nor 6 Share this post Link to post Share on other sites