600 pencils

600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?

Result

n =  3

Solution:

600=a+b+(a10) 610=a+b a>b>a10 0<a 0<b  z=610/3=6103203.3333  a1=204,b1=202,c1=194 a2=205,b2=200,c2=195 a3=206,b3=198,c3=196  n=3600=a+b+(a-10) \ \\ 610=a+b \ \\ a>b>a-10 \ \\ 0<a \ \\ 0<b \ \\ \ \\ z=610/3=\dfrac{ 610 }{ 3 } \doteq 203.3333 \ \\ \ \\ a_{ 1 }=204, b_{ 1 }=202, c_{ 1 }=194 \ \\ a_{ 2 }=205, b_{ 2 }=200, c_{ 2 }=195 \ \\ a_{ 3 }=206, b_{ 3 }=198, c_{ 3 }=196 \ \\ \ \\ n=3



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