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Who is wrong ?


jasen
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At a math class, a teacher gives his students 4 numbers, lets say the numbers are A, B, C and D
Then the teacher ask his students to make an equallity equation from the numbers.

Claudy says  2*a*b = c + 2*b
Leon says    a*b*c = 12 * c
Jemmy says   b*b + c*c = (a+b)^2
Thomas says  30*d = 6*b*c
Richard says a+b+c+d = a*a

Then the teacher says "Ok students, you are smart, but one of you is wrong"

If the numbers are positive integer not more than 100, Who is wrong, and what are the numbers ?
 

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statement given by jemmy :  b*b + c*c = (a+b)^2  is incorrect.

initially lets assume that Leon's statement is correct :     a*b*c = 12 * c

That means  a * b = 12

which means there are following possible values of a  & b

a = 6  b = 2 or a = 2 b = 6

or

a = 4 b = 3 or a = 3 b = 4

now take a = 6 and b = 2 then 

from   Claudy's statement   2*a*b = c + 2*b  => c = 20 

and on using  Thomas's statement : 30*d = 6*b*c => d = 8

and  Richard's  statement :  a+b+c+d = a*a => 6 + 2 + 20 + 8 = 6 * 6 => 36 = 36

only  Jemmy's statement :  b*b + c*c = (a+b)^2 is not satisfying this values.

so jemmy's statement is incorrect.

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