right triangle using 1 to 7

use 1 to 7, once only, so that the lines have the same total 

prove that the line totals cannot be below 12 or above 15 

prove that a line total of 14 is impossible

there are two solutions for sum = 13 and one for sums of 12 and 15 

students can be asked to find all of the solutions, once they have luxuriated in the glory of finding one solution of course...