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BEBRAS 2017 Grade 7-8 Round 2 Ext Question 7

BEBRAS · BEBRAS 2017 Grade 7-8 Round 2 Ext

Question 7

The famous blue diamond has been stolen and replaced by a green fake.

Question illustration

Exactly 2000 visitors entered its room one at a time, in a known order. Inspector Bebro asks selected visitors whether the diamond they saw was blue or green. Everyone answers truthfully except the thief, who says green. He wants to identify the thief with as few interviews as possible. Which promise can he truthfully make?
  1. I can guarantee finding the thief by interviewing fewer than 20 people.
  2. 20 interviews are insufficient unless lucky, but fewer than 200 always suffice.
  3. At least 200 and at most 1999 interviews are necessary.
  4. There is no guarantee; in the worst case every visitor must be interviewed.