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May
16
awarded  Caucus
Oct
11
asked Latin Squares - Proving the Unique number of Sudoku that can be generated
Sep
20
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)
Sep
20
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.
Sep
20
awarded  Commentator
Sep
20
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.
Sep
20
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.
Sep
20
comment Ordered quadruples in a grid
also mention that the question is a homework problem and tag it as such.
Sep
20
suggested suggested edit on Ordered quadruples in a grid
Sep
20
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.
Sep
20
revised Ordered quadruples in a grid
changed "integers" to "real numbers" as the property holds for real numbers as well
Sep
20
revised Ordered quadruples in a grid
deleted 160 characters in body
Sep
20
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.
Sep
20
answered Ordered quadruples in a grid
Sep
19
answered Degree choice — Math or physics
Sep
19
comment Degree choice — Math or physics
if you have cross-posted, also add the link to the original post.
Sep
18
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
Sep
18
awarded  Student
Sep
18
comment Why is the probability of having 2 boys 7/15?
It actually decreases the probability that the second child is a boy (because in the case if both boys being born in spring, ordering will not matter, resulting in one less case for the sample space).
Sep
18
revised Why is the probability of having 2 boys 7/15?
Removed a redundant part of the answer