Write the numbers 1,2,...,2n on a blackboard, where n is

Chapter 8, Problem 25E

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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.

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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.

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