Re: [algogeeks] Re: Math Puzzle
solution is =3 with the condition p!=0 and q!=0 and r!=0 Ashima M.Sc.(Tech)Information Systems 4th year BITS Pilani Rajasthan On Thu, Sep 15, 2011 at 10:38 PM, Piyush Grover wrote: > @abhinav... > > it's not about being over smart or to show someone or to prove someone > anything. It's just that > you should not take any assumptions by yourself or if you do you should > specify clearly. > If u r asked this question in an interview and you give the answer 3 > without telling your assumption, u r done!! > > And if you are living in the programming world, you need to take care of > all the possible scenarios otherwise u will end up throwing exceptions and > segmentation faults. > > > > On Thu, Sep 15, 2011 at 10:32 PM, Don wrote: > >> Right, and in every proof above, at some point there is a possible >> division by zero. Therefore the proof is not valid in cases where R or >> P or Q are zero, and there are infinitely many such cases. >> The problem states P+Q+R=0 as the only constraint. There are >> infinitely many cases which fit that constraint where the expression >> is not equal to 3. >> Don >> >> On Sep 15, 11:57 am, abhinav gupta wrote: >> > u cnt divide a number by 0..that thing is self undrstod >> > >> > On Thu, Sep 15, 2011 at 9:49 AM, Piyush Grover < >> piyush4u.iit...@gmail.com>wrote: >> > >> > >> > >> > > Don is right >> > >> > > if R = 0, P = 1 and Q = -1 then the given expression is UNDEFINED!!! >> > >> > > On Thu, Sep 15, 2011 at 10:16 PM, abhinav gupta < >> guptaabhinav...@gmail.com >> > > > wrote: >> > >> > >> Shut up...its 3,, >> > >> > >> On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: >> > >> > >>> It might be 3, but it doesn't have to be 3. >> > >>> Don >> > >> > >>> On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN >> wrote: >> > >>> > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? >> > >> > >>> > how to solve this?? >> > >> > >>> -- >> > >>> You received this message because you are subscribed to the Google >> Groups >> > >>> "Algorithm Geeks" group. >> > >>> To post to this group, send email to algogeeks@googlegroups.com. >> > >>> To unsubscribe from this group, send email to >> > >>> algogeeks+unsubscr...@googlegroups.com. >> > >>> For more options, visit this group at >> > >>>http://groups.google.com/group/algogeeks?hl=en. >> > >> > >> -- >> > >> @ |3 # ! /\/ @ \./ >> > >> > >> -- >> > >> You received this message because you are subscribed to the Google >> Groups >> > >> "Algorithm Geeks" group. >> > >> To post to this group, send email to algogeeks@googlegroups.com. >> > >> To unsubscribe from this group, send email to >> > >> algogeeks+unsubscr...@googlegroups.com. >> > >> For more options, visit this group at >> > >>http://groups.google.com/group/algogeeks?hl=en. >> > >> > > -- >> > > You received this message because you are subscribed to the Google >> Groups >> > > "Algorithm Geeks" group. >> > > To post to this group, send email to algogeeks@googlegroups.com. >> > > To unsubscribe from this group, send email to >> > > algogeeks+unsubscr...@googlegroups.com. >> > > For more options, visit this group at >> > >http://groups.google.com/group/algogeeks?hl=en. >> > >> > -- >> > @ |3 # ! /\/ @ \./ >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> >> > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: Math Puzzle
@abhinav... it's not about being over smart or to show someone or to prove someone anything. It's just that you should not take any assumptions by yourself or if you do you should specify clearly. If u r asked this question in an interview and you give the answer 3 without telling your assumption, u r done!! And if you are living in the programming world, you need to take care of all the possible scenarios otherwise u will end up throwing exceptions and segmentation faults. On Thu, Sep 15, 2011 at 10:32 PM, Don wrote: > Right, and in every proof above, at some point there is a possible > division by zero. Therefore the proof is not valid in cases where R or > P or Q are zero, and there are infinitely many such cases. > The problem states P+Q+R=0 as the only constraint. There are > infinitely many cases which fit that constraint where the expression > is not equal to 3. > Don > > On Sep 15, 11:57 am, abhinav gupta wrote: > > u cnt divide a number by 0..that thing is self undrstod > > > > On Thu, Sep 15, 2011 at 9:49 AM, Piyush Grover < > piyush4u.iit...@gmail.com>wrote: > > > > > > > > > Don is right > > > > > if R = 0, P = 1 and Q = -1 then the given expression is UNDEFINED!!! > > > > > On Thu, Sep 15, 2011 at 10:16 PM, abhinav gupta < > guptaabhinav...@gmail.com > > > > wrote: > > > > >> Shut up...its 3,, > > > > >> On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > > > > >>> It might be 3, but it doesn't have to be 3. > > >>> Don > > > > >>> On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > > >>> > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > > > >>> > how to solve this?? > > > > >>> -- > > >>> You received this message because you are subscribed to the Google > Groups > > >>> "Algorithm Geeks" group. > > >>> To post to this group, send email to algogeeks@googlegroups.com. > > >>> To unsubscribe from this group, send email to > > >>> algogeeks+unsubscr...@googlegroups.com. > > >>> For more options, visit this group at > > >>>http://groups.google.com/group/algogeeks?hl=en. > > > > >> -- > > >> @ |3 # ! /\/ @ \./ > > > > >> -- > > >> You received this message because you are subscribed to the Google > Groups > > >> "Algorithm Geeks" group. > > >> To post to this group, send email to algogeeks@googlegroups.com. > > >> To unsubscribe from this group, send email to > > >> algogeeks+unsubscr...@googlegroups.com. > > >> For more options, visit this group at > > >>http://groups.google.com/group/algogeeks?hl=en. > > > > > -- > > > You received this message because you are subscribed to the Google > Groups > > > "Algorithm Geeks" group. > > > To post to this group, send email to algogeeks@googlegroups.com. > > > To unsubscribe from this group, send email to > > > algogeeks+unsubscr...@googlegroups.com. > > > For more options, visit this group at > > >http://groups.google.com/group/algogeeks?hl=en. > > > > -- > > @ |3 # ! /\/ @ \./ > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
[algogeeks] Re: Math Puzzle
Right, and in every proof above, at some point there is a possible division by zero. Therefore the proof is not valid in cases where R or P or Q are zero, and there are infinitely many such cases. The problem states P+Q+R=0 as the only constraint. There are infinitely many cases which fit that constraint where the expression is not equal to 3. Don On Sep 15, 11:57 am, abhinav gupta wrote: > u cnt divide a number by 0..that thing is self undrstod > > On Thu, Sep 15, 2011 at 9:49 AM, Piyush Grover > wrote: > > > > > Don is right > > > if R = 0, P = 1 and Q = -1 then the given expression is UNDEFINED!!! > > > On Thu, Sep 15, 2011 at 10:16 PM, abhinav gupta > > wrote: > > >> Shut up...its 3,, > > >> On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > > >>> It might be 3, but it doesn't have to be 3. > >>> Don > > >>> On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > >>> > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > >>> > how to solve this?? > > >>> -- > >>> You received this message because you are subscribed to the Google Groups > >>> "Algorithm Geeks" group. > >>> To post to this group, send email to algogeeks@googlegroups.com. > >>> To unsubscribe from this group, send email to > >>> algogeeks+unsubscr...@googlegroups.com. > >>> For more options, visit this group at > >>>http://groups.google.com/group/algogeeks?hl=en. > > >> -- > >> @ |3 # ! /\/ @ \./ > > >> -- > >> You received this message because you are subscribed to the Google Groups > >> "Algorithm Geeks" group. > >> To post to this group, send email to algogeeks@googlegroups.com. > >> To unsubscribe from this group, send email to > >> algogeeks+unsubscr...@googlegroups.com. > >> For more options, visit this group at > >>http://groups.google.com/group/algogeeks?hl=en. > > > -- > > You received this message because you are subscribed to the Google Groups > > "Algorithm Geeks" group. > > To post to this group, send email to algogeeks@googlegroups.com. > > To unsubscribe from this group, send email to > > algogeeks+unsubscr...@googlegroups.com. > > For more options, visit this group at > >http://groups.google.com/group/algogeeks?hl=en. > > -- > @ |3 # ! /\/ @ \./ -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: Math Puzzle
dude dats outside the domain of the qs...dont be oversmart. On Thu, Sep 15, 2011 at 9:49 AM, Don wrote: > No, not at all. Here is a trivial counterexample: > > P = Q = R = 0 > > Don > > On Sep 15, 11:46 am, abhinav gupta wrote: > > Shut up...its 3,, > > > > > > > > On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > > > It might be 3, but it doesn't have to be 3. > > > Don > > > > > On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > > > > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > > > > > how to solve this?? > > > > > -- > > > You received this message because you are subscribed to the Google > Groups > > > "Algorithm Geeks" group. > > > To post to this group, send email to algogeeks@googlegroups.com. > > > To unsubscribe from this group, send email to > > > algogeeks+unsubscr...@googlegroups.com. > > > For more options, visit this group at > > >http://groups.google.com/group/algogeeks?hl=en. > > > > -- > > @ |3 # ! /\/ @ \./ > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- @ |3 # ! /\/ @ \./ -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: Math Puzzle
u cnt divide a number by 0..that thing is self undrstod On Thu, Sep 15, 2011 at 9:49 AM, Piyush Grover wrote: > Don is right > > if R = 0, P = 1 and Q = -1 then the given expression is UNDEFINED!!! > > > > On Thu, Sep 15, 2011 at 10:16 PM, abhinav gupta > wrote: > >> Shut up...its 3,, >> >> >> On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: >> >>> It might be 3, but it doesn't have to be 3. >>> Don >>> >>> On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: >>> > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? >>> > >>> > how to solve this?? >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "Algorithm Geeks" group. >>> To post to this group, send email to algogeeks@googlegroups.com. >>> To unsubscribe from this group, send email to >>> algogeeks+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/algogeeks?hl=en. >>> >>> >> >> >> -- >> @ |3 # ! /\/ @ \./ >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > -- @ |3 # ! /\/ @ \./ -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
[algogeeks] Re: Math Puzzle
No, not at all. Here is a trivial counterexample: P = Q = R = 0 Don On Sep 15, 11:46 am, abhinav gupta wrote: > Shut up...its 3,, > > > > On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > > It might be 3, but it doesn't have to be 3. > > Don > > > On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > > > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > > > how to solve this?? > > > -- > > You received this message because you are subscribed to the Google Groups > > "Algorithm Geeks" group. > > To post to this group, send email to algogeeks@googlegroups.com. > > To unsubscribe from this group, send email to > > algogeeks+unsubscr...@googlegroups.com. > > For more options, visit this group at > >http://groups.google.com/group/algogeeks?hl=en. > > -- > @ |3 # ! /\/ @ \./ -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: Math Puzzle
Don is right if R = 0, P = 1 and Q = -1 then the given expression is UNDEFINED!!! On Thu, Sep 15, 2011 at 10:16 PM, abhinav gupta wrote: > Shut up...its 3,, > > > On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > >> It might be 3, but it doesn't have to be 3. >> Don >> >> On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: >> > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? >> > >> > how to solve this?? >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> >> > > > -- > @ |3 # ! /\/ @ \./ > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: Math Puzzle
Shut up...its 3,, On Thu, Sep 15, 2011 at 9:43 AM, Don wrote: > It might be 3, but it doesn't have to be 3. > Don > > On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > > > how to solve this?? > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- @ |3 # ! /\/ @ \./ -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
[algogeeks] Re: Math Puzzle
It might be 3, but it doesn't have to be 3. Don On Sep 14, 11:56 pm, NAGARAJAN SIVARAMAN wrote: > if P+Q+R= 0 then P2 /QR + Q2/PR + R2/PQ = ?? > > how to solve this?? -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: math puzzle
3x+4y = 60 can be expressed as 15 -y = 3x+3y -45 i.e, 15-y = 3(x+y-15) which implies tht for every value of x,y in the above eq 15-y is divisible by 3 On Sun, Aug 28, 2011 at 10:03 PM, Dave wrote: > @Harhsit: Normally, 0 is not considered positive. > > Dave > > On Aug 28, 10:45 am, harshit sethi wrote: > > sorry 6 solutions y=15,12,9,6,3,0 > > and x=0,4,8,12,16,20 respectively > > > > On 8/28/11, harshit sethi wrote: > > > > > > > > > maximum value of y satisfying this is y=15 and for that x=0; > > > > > now decrease y by 3 and increase x by 4 ,you will have x and y > > > satisfying the equation. > > > > > keep on doing this till you reach minimum value of y i.e 0 > > > > > this you can do 5 times decreasing y=15 by 3 every time > > > > > so there will be 5 solutions . > > > > > On 8/28/11, Piyush Grover wrote: > > >> 3x+4y = 60 > > >> it's a straight line equation whose x intercept is 20 and y intercept > is > > >> 15. > > >> Draw it in first quadrant > > >> (as x, y are positive integers) > > >> now x = (60 - 4y)/3 = 4(15-y)/3 > > >> now for y = 1, 2...15 you need to check whether (15-y) is divisible by > 3 > > >> or > > >> not. It's simple y = 3, 6, 9, 12 > > > > >> -Piyush > > > > >> On Sun, Aug 28, 2011 at 6:38 PM, Dave > wrote: > > > > >>> @Sivaviknesh: The smallest values of x and y are 1. The largest value > > >>> of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is > > >>> an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a > > >>> multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. > > >>> Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding > values > > >>> of x. > > > > >>> Dave > > > > >>> On Aug 28, 7:46 am, sivaviknesh s wrote: > > >>> > *Find the number of solutions for 3x+4y=60, if x and y are positive > > >>> > integers.* > > > > >>> > Is there any standard method for solving these type of ques ..or > only > > >>> trial > > >>> > and error ??? > > > > >>> > -- > > >>> > Regards, > > >>> > $iva > > > > >>> -- > > >>> You received this message because you are subscribed to the Google > > >>> Groups > > >>> "Algorithm Geeks" group. > > >>> To post to this group, send email to algogeeks@googlegroups.com. > > >>> To unsubscribe from this group, send email to > > >>> algogeeks+unsubscr...@googlegroups.com. > > >>> For more options, visit this group at > > >>>http://groups.google.com/group/algogeeks?hl=en. > > > > >> -- > > >> You received this message because you are subscribed to the Google > Groups > > >> "Algorithm Geeks" group. > > >> To post to this group, send email to algogeeks@googlegroups.com. > > >> To unsubscribe from this group, send email to > > >> algogeeks+unsubscr...@googlegroups.com. > > >> For more options, visit this group at > > >>http://groups.google.com/group/algogeeks?hl=en.- Hide quoted text - > > > > - Show quoted text - > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- Rishabbh A Dua -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
[algogeeks] Re: math puzzle
@Harhsit: Normally, 0 is not considered positive. Dave On Aug 28, 10:45 am, harshit sethi wrote: > sorry 6 solutions y=15,12,9,6,3,0 > and x=0,4,8,12,16,20 respectively > > On 8/28/11, harshit sethi wrote: > > > > > maximum value of y satisfying this is y=15 and for that x=0; > > > now decrease y by 3 and increase x by 4 ,you will have x and y > > satisfying the equation. > > > keep on doing this till you reach minimum value of y i.e 0 > > > this you can do 5 times decreasing y=15 by 3 every time > > > so there will be 5 solutions . > > > On 8/28/11, Piyush Grover wrote: > >> 3x+4y = 60 > >> it's a straight line equation whose x intercept is 20 and y intercept is > >> 15. > >> Draw it in first quadrant > >> (as x, y are positive integers) > >> now x = (60 - 4y)/3 = 4(15-y)/3 > >> now for y = 1, 2...15 you need to check whether (15-y) is divisible by 3 > >> or > >> not. It's simple y = 3, 6, 9, 12 > > >> -Piyush > > >> On Sun, Aug 28, 2011 at 6:38 PM, Dave wrote: > > >>> @Sivaviknesh: The smallest values of x and y are 1. The largest value > >>> of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is > >>> an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a > >>> multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. > >>> Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding values > >>> of x. > > >>> Dave > > >>> On Aug 28, 7:46 am, sivaviknesh s wrote: > >>> > *Find the number of solutions for 3x+4y=60, if x and y are positive > >>> > integers.* > > >>> > Is there any standard method for solving these type of ques ..or only > >>> trial > >>> > and error ??? > > >>> > -- > >>> > Regards, > >>> > $iva > > >>> -- > >>> You received this message because you are subscribed to the Google > >>> Groups > >>> "Algorithm Geeks" group. > >>> To post to this group, send email to algogeeks@googlegroups.com. > >>> To unsubscribe from this group, send email to > >>> algogeeks+unsubscr...@googlegroups.com. > >>> For more options, visit this group at > >>>http://groups.google.com/group/algogeeks?hl=en. > > >> -- > >> You received this message because you are subscribed to the Google Groups > >> "Algorithm Geeks" group. > >> To post to this group, send email to algogeeks@googlegroups.com. > >> To unsubscribe from this group, send email to > >> algogeeks+unsubscr...@googlegroups.com. > >> For more options, visit this group at > >>http://groups.google.com/group/algogeeks?hl=en.- Hide quoted text - > > - Show quoted text - -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: math puzzle
sorry 6 solutions y=15,12,9,6,3,0 and x=0,4,8,12,16,20 respectively On 8/28/11, harshit sethi wrote: > maximum value of y satisfying this is y=15 and for that x=0; > > now decrease y by 3 and increase x by 4 ,you will have x and y > satisfying the equation. > > keep on doing this till you reach minimum value of y i.e 0 > > this you can do 5 times decreasing y=15 by 3 every time > > so there will be 5 solutions . > > On 8/28/11, Piyush Grover wrote: >> 3x+4y = 60 >> it's a straight line equation whose x intercept is 20 and y intercept is >> 15. >> Draw it in first quadrant >> (as x, y are positive integers) >> now x = (60 - 4y)/3 = 4(15-y)/3 >> now for y = 1, 2...15 you need to check whether (15-y) is divisible by 3 >> or >> not. It's simple y = 3, 6, 9, 12 >> >> -Piyush >> >> On Sun, Aug 28, 2011 at 6:38 PM, Dave wrote: >> >>> @Sivaviknesh: The smallest values of x and y are 1. The largest value >>> of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is >>> an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a >>> multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. >>> Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding values >>> of x. >>> >>> Dave >>> >>> On Aug 28, 7:46 am, sivaviknesh s wrote: >>> > *Find the number of solutions for 3x+4y=60, if x and y are positive >>> > integers.* >>> > >>> > Is there any standard method for solving these type of ques ..or only >>> trial >>> > and error ??? >>> > >>> > -- >>> > Regards, >>> > $iva >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups >>> "Algorithm Geeks" group. >>> To post to this group, send email to algogeeks@googlegroups.com. >>> To unsubscribe from this group, send email to >>> algogeeks+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/algogeeks?hl=en. >>> >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> >> > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: math puzzle
maximum value of y satisfying this is y=15 and for that x=0; now decrease y by 3 and increase x by 4 ,you will have x and y satisfying the equation. keep on doing this till you reach minimum value of y i.e 0 this you can do 5 times decreasing y=15 by 3 every time so there will be 5 solutions . On 8/28/11, Piyush Grover wrote: > 3x+4y = 60 > it's a straight line equation whose x intercept is 20 and y intercept is 15. > Draw it in first quadrant > (as x, y are positive integers) > now x = (60 - 4y)/3 = 4(15-y)/3 > now for y = 1, 2...15 you need to check whether (15-y) is divisible by 3 or > not. It's simple y = 3, 6, 9, 12 > > -Piyush > > On Sun, Aug 28, 2011 at 6:38 PM, Dave wrote: > >> @Sivaviknesh: The smallest values of x and y are 1. The largest value >> of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is >> an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a >> multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. >> Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding values >> of x. >> >> Dave >> >> On Aug 28, 7:46 am, sivaviknesh s wrote: >> > *Find the number of solutions for 3x+4y=60, if x and y are positive >> > integers.* >> > >> > Is there any standard method for solving these type of ques ..or only >> trial >> > and error ??? >> > >> > -- >> > Regards, >> > $iva >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Algorithm Geeks" group. >> To post to this group, send email to algogeeks@googlegroups.com. >> To unsubscribe from this group, send email to >> algogeeks+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/algogeeks?hl=en. >> >> > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: math puzzle
3x+4y = 60 it's a straight line equation whose x intercept is 20 and y intercept is 15. Draw it in first quadrant (as x, y are positive integers) now x = (60 - 4y)/3 = 4(15-y)/3 now for y = 1, 2...15 you need to check whether (15-y) is divisible by 3 or not. It's simple y = 3, 6, 9, 12 -Piyush On Sun, Aug 28, 2011 at 6:38 PM, Dave wrote: > @Sivaviknesh: The smallest values of x and y are 1. The largest value > of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is > an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a > multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. > Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding values > of x. > > Dave > > On Aug 28, 7:46 am, sivaviknesh s wrote: > > *Find the number of solutions for 3x+4y=60, if x and y are positive > > integers.* > > > > Is there any standard method for solving these type of ques ..or only > trial > > and error ??? > > > > -- > > Regards, > > $iva > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to algogeeks@googlegroups.com. > To unsubscribe from this group, send email to > algogeeks+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
[algogeeks] Re: math puzzle
@Sivaviknesh: The smallest values of x and y are 1. The largest value of y is (60 - 3) / 4 = 14. Solve for x: x = (60 - 4y) / 3. Since x is an integer, 60 - 4y must be a multiple of 3. Since 60 - 3y is a multiple of 3, (60 - 4y) - (60 - 3y) = y must be a multiple of 3. Thus, y = 3, 6, 9, 12. Then you can solve for the corresponding values of x. Dave On Aug 28, 7:46 am, sivaviknesh s wrote: > *Find the number of solutions for 3x+4y=60, if x and y are positive > integers.* > > Is there any standard method for solving these type of ques ..or only trial > and error ??? > > -- > Regards, > $iva -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
