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Scorpion Power  Scorpion Power 
12052012 02:59 AM 6 years ago  Post 1 
red_z06 rrProfessor Dumont, NJ  Find this 3 digit number that satisfies following condition.1. 10th place number is 62. Switching 100th and 1th number causes the new number to be smaller than the original by 297.3. Switching 100th and 1th of the original number and adding 179 to it will turn the new number to have same 100th 10th and 1th digits. For example 111, 222 etc.www.JustinJee.com  

12052012 03:22 AM 6 years ago  Post 2 
utahbob rrVeteran St. George Utah 
 

12052012 04:40 AM 6 years ago  Post 3 
baldgeek rrApprentice New Zealand  562  

12052012 04:48 AM 6 years ago  Post 4 
PsychoZ rrApprentice Northern, CA  42, it is the answer to everything including life itself.Tea Parties are for little girls with imaginary friends  

12052012 11:20 AM 6 years ago  Post 5 
JoseA rrNovice South Chicago  8765309I'll email my pay pal info...The ignored one  

12052012 11:27 AM 6 years ago  Post 6 
red_z06 rrProfessor Dumont, NJ  Ding Ding Ding. We have a correct answer.Very nice Baldgeek.www.JustinJee.com  

12052012 03:56 PM 6 years ago  Post 7 
PsychoZ rrApprentice Northern, CA  http://en.wikipedia.org/wiki/8675309/Jenny8765309  

12052012 04:02 PM 6 years ago  Post 8 
titillater rrApprentice Duncan B.C  How is that a 3 digit number?  

12062012 12:33 PM 6 years ago  Post 9 
Climax rrVeteran West London, United Kingdom  That's a fun problem!I'm not sure if this is the best way to solve it, but this is what I did... If there is a better method, then please post!Let the answer be N, and in terms of digits this would be represented as X6Y  So all we need to do is find X and Y...So from point (1) you can form the following equation,N = 100X + 60 + YNow taking point (2) into account you get,100Y + 60 + X + 297 = N100Y + 60 + X +297 = 100X + 60 + YWhich simplifies to,X  Y = 3 (Remember this as equation 1)OK, you just need one more equation relating X to Y and you can then solve them as a simultaneous pairFrom point (3)100Y + 60 + X + 179 = 100Z +10Z + ZWhere Z represents the digits in either 111 to 999 (i.e. ZZZ, as described in point 3 of the problem)This simplifies to,100Y + 60 + X + 179 = 111Z (Remember this as equation 2)You still need to figure out Z, here's what I did...We know that in the answer the middle digit is "6" (as we have been told this in the question)We also know (in symbolic terms) that Y6X + 179 = ZZZNow consider the middle digits, here 6 + 7 = 13. So it would appear that the middle Z might be a "3" with a carry that ripples up (13 = 10 + 3, or 3 carry 1). It also possible that there was a "carry up" from the lower down X + 9 component, in which case the middle Z would be a 4.So we now know that Z is either 3 or 4. Now if you think about it, it can't be a "3" as there is always a carry from the lowest digit. Why, well if Z is 3 or 4, then the X + 9 component will always generate a carry!So Z = 4This means that equation 2 becomes,100Y + 60 + X + 179 = 444Which simplifies to,100Y + X = 205 (Remember this as equation 3)We now have 2 equations in X and Y100Y + X = 205 X  Y = 3 (this was equation 1 from above)Let's find X...X = 3 + YThen substitute in to equation 3,100Y + (3 + Y) = 205 101Y = 202 Y = 2Then as X = 3 + Y,X = 5Which means that the answer is 562I'm sure there must be a simpler way, any ideas? Electronics, Physics, Helicopters, Fixing Things...  

12062012 02:00 PM 6 years ago  Post 10 
Shawn Pierce rrVeteran Galliano, Louisiana  Yeah, i did 3rd one first. 222179=43 333179=154 444179=165 555179=376 666179=487 777179=598 888179=709 999179=820444 is the only one with a 6 in middle. reverse numbers and double check 562265=297  

12062012 02:07 PM 6 years ago  Post 11 
Climax rrVeteran West London, United Kingdom  I guess what I was trying to do was to formulate a couple of simultaneous equations to solve the problem without have to do it heuristically at any stage. i.e. avoiding the "try out the possibilities" approach that's made easy by step 3...Which I couldn't really do!Electronics, Physics, Helicopters, Fixing Things...  

12062012 02:49 PM 6 years ago  Post 12 
mr dan rrVeteran Stockton Calif  Wow Im very impressed (Yawn!)
 

12062012 04:48 PM 6 years ago  Post 13 
red_z06 rrProfessor Dumont, NJ  I started it the way Climax did. But, forgot thatN = 100Y + 60 + X + 297LOLSo I ended up with 2 eq and 3 unknowns. Someone solved it in a simpler fashion.BTW, the original (Korean) problem stated this was from a 2nd grade math problem. It is hard to believe. But, considering that, perhaps they were seeking the methond Shawn was using. I hated to do the plug in method but in this case it only took 9 tries.Nice one Shawn.www.JustinJee.com  

12062012 05:11 PM 6 years ago  Post 14 
red_z06 rrProfessor Dumont, NJ  This is how one guy solved it.A = 100th digitB = 1th digitB6A+179=CCCSince A is 100th digit, it can't be zero. If A can't be zero, then C=4 (for the values of A 1 through 9)So, 444179=265B=2 A=5Answer is 562. www.JustinJee.com  

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