Solution Found!
Write the numbers 1,2,...,2n on a blackboard, where n is
Chapter 8, Problem 25E(choose chapter or problem)
Problem 25E
Write the numbers 1,2,...,2n on a blackboard, where n is an odd integer. Pick any two of the numbers, j and k, write |j ‒ k| on the board and erase j and k. Continue this process until only one integer is written on the board. Prove that this integer must he odd.
Questions & Answers
QUESTION:
Problem 25E
Write the numbers 1,2,...,2n on a blackboard, where n is an odd integer. Pick any two of the numbers, j and k, write |j ‒ k| on the board and erase j and k. Continue this process until only one integer is written on the board. Prove that this integer must he odd.
ANSWER:
SOLUTION
Step 1
Write the numbers 1,2,3,...2n,where n is odd.
We have there are ‘n’ odd numbers in between 1 and 2n and ‘n’ is odd.
Consider the following cases.