Can you get it right for this logic question?

Logic Level 2

There are 2018 statements in the following list:

  • Statement 1: "Only 1 statement on this list is false."
  • Statement k , 2 ≤ k ≤ 2017 : k,\ 2\le k\le 2017: "Exactly k k statements on this list are false."
  • Statement 2018: "All the statements on this list are false."

Given that statement M M can be true, find the sum of all such M . M.

2018 ( 2017 ) ( 2018 ) 2 \frac{(2017)(2018)}{2} None of the statements can be true. 2017

Chan Lye Lee by Chan Lye Lee , 44, Singapore

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1 solution

Chan Lye Lee
Apr 13, 2018

Since any two statements in the list contradict to each other, no two statements can be true simultaneously. This means that only 1 statement on the list can be true, and hence the other 2017 statements are false. Thus, M = 2017 M=2017 .

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