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The 10th distance (Posted on 2021-09-06) Difficulty: 3 of 5
Five points are located on a certain straight line Nine pairwise distances are known: 2,4,5,7,12,13,15,17,19

Find the 10th.

Based on Hoshino & McCurdy puzzle published in Crux Mathematicorum

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
semi-analytic | Comment 3 of 8 |
Similarly, I just did the following, involving some guessing: 
I guessed 19 was the whole span. If the points along the line are
0, a, b, c, d, then (a-0) + (b-a) + (c-b) + (d-c) =19 
where the ( ) terms must all be present in the complete list of 
10 distances.  But the first 4 given add to 18. (We can't go further than the 1st 4 because the sum gets too great or there's an endless recursive generation of smaller terms). Therefore we may substitute out each one, one at a time, and replace it with a number 1 larger as the missing distance. This makes the 4 "adjacent point" distances 
(3,4,5,7) or (2,5,5,7) or (2,4,6,7)  or (2,4,5,8). Only the last set generates the other distances:  12,13,15,17


Edited on September 6, 2021, 12:36 pm
  Posted by Steven Lord on 2021-09-06 11:23:03

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