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bio website scitemplar.wordpress.com
location India
age 23
visits member for 2 years, 3 months
seen Nov 22 at 0:54

Sep
30
awarded  Explainer
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).