COMC 2011 Problem 10
Source:
November 4, 2012
Problem Statement
Charlotte writes a test consisting of 100 questions, where the answer to each question is either TRUE or
FALSE. Charlotte’s teacher announces that for every five consecutive questions on the test, the answers to
exactly three of them are TRUE. Just before the test starts, the teacher whispers to Charlotte that the
answers to the first and last questions are both FALSE.
(a) Determine the number of questions for which the correct answer is TRUE.
(b) What is the correct answer to the sixth question on the test?
(c) Explain how Charlotte can correctly answer all 100 questions on the test.