5. Three numbers are stored in a computer's memory. Every second, the following operation is performed: each number in this triplet is replaced by the sum of the other two. For example, the triplet $(1 ; 3 ; 7)$ turns into $(10 ; 8 ; 4)$. What will be the difference between the largest and smallest number in the triplet obtained from the triplet (20; 1; 6) after 2016 seconds?
5. Answer: 19. Solution. Let the initial triplet be ( $a ; b ; c$). Since all numbers in the triplet are distinct, we will assume that $a<b<c$. In the next second, the triplet of numbers will look like this: $(b+c$; $a+c ; a+b)$. The largest number in this triplet is $b+c$, and the smallest is $a+b$. Their difference is $b+c-(a+b)=c-a$, i.e., it coincides with the initial difference between the largest and smallest numbers. Therefore, after 2016 seconds, the difference between the largest and smallest numbers in the triplet will be equal to the corresponding difference in the initial triplet of numbers, i.e., $20-1=19$. Grading criteria: correct reasoning provided, correct answer obtained - 7 points. Key pattern noticed, correct answer given, but no justification - 2 points.