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 Dec22 awarded Constituent Dec22 awarded Caucus Sep30 awarded Explainer May16 awarded Caucus Oct11 asked Latin Squares - Proving the Unique number of Sudoku that can be generated Sep20 comment Ordered quadruples in a grid Similarly, for $b_i$, lets compare the 1st two $\alpha_i$ in the first column. We have $\alpha_11$ = a11 + b11 + c1. $\alpha_12$ = a12 + b12 + c12. For both these to be part of the same quadruple (given that the 1st column is a quadruple), $a_12$ = 4$a_11$, $b_12$ = 2$b_11$ (as m = 2) Sep20 comment Ordered quadruples in a grid We already have 4 rows of ordered quadruples each with $c_i$ different. Now, we know that 3 columns are ordered quadruples. This means for any 2 of them in the same column, the constant term i.e $c_i$ must be the same (else they will not be an ordered tuple). For this assumption of 3 columns to be ordered quadruples, all $c_i$ must be the same. Sep20 awarded Commentator Sep20 comment Ordered quadruples in a grid Say c1 != c2. This means that for any 2 $\alpha_i$ in a column, the numbers will not be part of an ordered quadruple. Since we are comparing $c_i$ in two different rows, they must be all be equal. Sep20 revised Ordered quadruples in a grid The OP commented on my answer that a,b,c need not be integers. I have told him/her to change it but it has not been done. Hence, doing the honors. Sep20 comment Ordered quadruples in a grid also mention that the question is a homework problem and tag it as such. Sep20 suggested approved edit on Ordered quadruples in a grid Sep20 comment Ordered quadruples in a grid @AriaFitzpatrick I have modified in my answer that a,b,c are real numbers and suggest that you also change it in the question. Sep20 revised Ordered quadruples in a grid changed "integers" to "real numbers" as the property holds for real numbers as well Sep20 revised Ordered quadruples in a grid deleted 160 characters in body Sep20 comment Ordered quadruples in a grid @AriaFitzpatrick it was mentioned in your question that a,b,c are integers. Hence I added it. Also, this answer is valid regardless of whether a,b,c are integers. Sep20 answered Ordered quadruples in a grid Sep19 answered Degree choice — Math or physics Sep19 comment Degree choice — Math or physics if you have cross-posted, also add the link to the original post. Sep18 comment Why is the probability of having 2 boys 7/15? Oops.. I was thinking in terms on 8/15 > 7/15. Sorry for the scramble. :P