1-2008 written on blackboard, replace two numbers with their difference
Source: XIV May Olympiad (Olimpiada de Mayo) 2008 L1 P3
September 22, 2022
combinatoricsgame
Problem Statement
On a blackboard are written all the integers from to inclusive. Two numbers are deleted and their difference is written. For example, if you erase and , you write . This continues, erasing two numbers and writing their difference, until only one number remains. Determine if the number left at the end can be . What about ? In each case, if the answer is affirmative, indicate a sequence with that final number, and if it is negative, explain why.