John was given a math question.
Find a solution to \(a+bcd=b+acd=c+abd=d+abc=2\)
He solves it as follows:
Step 1: Rearrange into: \(bcd-acd=b-a\)
Step 2: Factorise into: \(cd(b-a)=b-a\)
Step 3: Divide: \(cd=1\)
Step 4: Apply to each and every equation: \(ab=ac=ad=bc=bd=cd=1\)
Step 5: Compare to get \(a=b=c=d=1\) as one of the solution.
However, his teacher marked him wrong!
What went wrong?