Question 1115529
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                It is a nice logic problem.



<pre>
1.  From the condition, it is clear that the amounts each person spent for presents, each (amount) is a perfect square of cents.



2.  If x and y  are spendings for some (any) of the three couples, then

    x^2 - y^2 = 75,    according to the condition,  or

    (x+y)(x-y) = 75.   (and we remember that the greater value is the wife's spending !)


    For integer positive  x and y  it gives these and only these opportunities


        x + y = 75
        x - y =  1     with the solution  x= 38,  y= 37  
    OR
        x + y = 25
        x - y =  3     with the solution  x= 14,  y= 11
    OR  
        x + y = 15
        x - y =  5     with the solution  x= 10,  y= 5.


    Of these solutions,  the only pair  (38,37)  has the difference of 1,  so it gives a clue to me to conclude that

                         Ann is the wife to Bill Brown.



3.  But in order for to make this conclusion ABSOLUTELY CORRECT, I must <U>EXCLUDE</U> that the other couples fall in the same pair/solution (38,37).

    Fortunately, the condition gives me rationality to make this conclusion.

    Indeed, it says that "Betty bought one less present than Joe Jones", which means that Betty is of the pair (10,5), while Joe Jones is 

    of the pair (14,11).  So, I really can conclude that Ann is the wife to Bill Brown.



4.  Finally, from the condition, it is also clear that Betty <U>IS NOT</U>  the wife to Joe Jones.



5.  It leaves <U>only one opportunity</U>  for Mary to be Mary Jones.
</pre>

Solved.


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Many thanks for submitting this nice problem.


It was truly delight for me to solve it.