All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Ten to five (Posted on 2018-07-30)
You are given a set of 10 numbers that represent all possible pairwise sums of certain five numbers.

Devise a strategy to find the original five numbers.

Provide a numerical example.

Comments: ( Back to comment list | You must be logged in to post comments.)
 solution (spoiler) | Comment 1 of 7

60 83 85 87 89 100 102 112 125 129

These add up to 972. As each number is counted four times, the total of the five numbers is 972/4 = 243.

The largest of the ten is 129 and the smallest is 60. These are the sums of the largest two and the smallest two of the five, respectively, so subtracting the total of these two, representing four of the five, from the total of the five, 243, will give the value of the middle of the five: 243 - (129+60) = 54.

The third largest of the ten will be the middle plus the largest (of the five). So in this case 112 = 54 + 58, making 58 the second largest number.  Then 129 - 58 gives you the largest number, 71.

Symmetrically with the preceding paragraph, the third smallest of the ten will be the middle plus the smallest of the five. In this case 85 = 54 + 31, making 31 the second smallest of the five. Then 60 - 31 gives you 29, the smallest of the five.

In this case we have figured out

29 31 54 58 71

 Posted by Charlie on 2018-07-30 11:03:24

 Search: Search body:
Forums (0)