Question 1210231
.
Find the number of ways filling in a 4 \times 4 grid, such that
* Each cell contains a 0 or a 1.
* The sum of the numbers in each row and each column is at least 2.
An example is shown below.

0110
1010
0011
1111
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The way, how the problem is worded, is ambiguous. 


The ambiguous is this sentence "The sum of the numbers in each row and each column is at least 2."


One interpretation is that the sum of the numbers in each row and the sum of the numbers in each column 
should be at least 2 - separately for each of the two sums.


Another interpretation is that the one combined sum (of the numbers in each row and in each column) 
should be at least 2 as one total sum of 7 addends.


The given example does not provide a possibility/opportunity to select one of the two possible interpretations.


When a professional Math writer creates a problem, he/she ALWAYS will find a way to avoid ambiguity.



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XXXXXXXXXXXXXX - - - It is his or her PROFESSIONAL DUTY. - - - XXXXXXXXXXXXX


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Otherwise, this writer is NOT a professional.


     
Best regards.