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Permuted sums (Posted on 2020-11-30) Difficulty: 2 of 5
A set contains four numbers. The six pairwise sums of distinct elements of the set, in no particular order, are 189, 320, 287, 264, x, and y. Find the greatest possible value of: x + y.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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Solution Solution, part 2 | Comment 2 of 7 |
The required greatest possible sum of x+y is 761

Case 1:
a   b   c   d   x   y
83 106 181 237 343 418

 a+b a+c a+d b+c b+d c+d
189 264 320 287 343 418

 and the sum is:  761

Case 2 yields no solutions.

Code follows:

# case 1
theSum = 0
for a in range (190):
    b = 189 - a
    c = 264 - a
    d = 320 - a
    if (b+c) != 287:
        continue
    x = b+d
    y = c+d
    theSum = x+y
    print('Case 1: ')
    print('a   b   c   d   x   y')
    print(a,b,c,d,x,y)
    print('\n', 'a+b a+c a+d b+c b+d c+d')
    print(a+b,a+c,a+d,b+c,b+d,c+d)
    print('\n', 'and the sum is: ', theSum)



# case 2   provides no solutions
theSum = 0
for a in range (190):        
    b = 189 - a
    c = 264 - a
    d = 287 - a
    if (b+c) != 320:
        continue
    x = b+d
    y = c+d
    theSum = x+y
    print('Case 2: ')
    print('a   b   c   d   x   y')
    print(a,b,c,d,x,y)
    print('\n', 'a+b a+c a+d b+c b+d c+d')
    print(a+b,a+c,a+d,b+c,b+d,c+d)
    print('\n', 'and the sum is: ', theSum)
   

  Posted by Larry on 2020-11-30 09:58:19
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