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BEBRAS 2017 Grade 5-6 Round 2 Ext Question 10

BEBRAS · BEBRAS 2017 Grade 5-6 Round 2 Ext

Question 10

Oh no! The famous Blue Diamond was stolen from the museum today: a thief replaced it with a fake green diamond.

Question illustration

There were 2000 visitors, entering the diamond room one at a time. Inspector Bebro has their names in visiting order. He asks each interviewed visitor the same question: “When you saw the diamond, was it blue or green?” Everyone answers honestly, except the thief, who says it was green. Bebro is clever and interviews as few people as possible. Which statement can he truthfully make?
  1. I guarantee I can find the thief by interviewing fewer than 20 people.
  2. Interviewing only 20 people is not enough unless I am lucky, but I am sure I can find the thief with fewer than 200 interviews.
  3. This will be difficult: I need at least 200 and at most 1999 interviews.
  4. I cannot promise anything. If unlucky, I may have to interview every visitor.