Three people sit at a round table, facing inwards, towards the centre of the table. No two of them are the same age. Each of them says “I am younger than the person to my left.” 1.
What is the greatest possible number of people telling the truth? 2. What is the smallest possible number of people telling the truth? 1. The oldest person must be lying, so the maximum is 2.
Here is an example with 2 people telling the truth: 30-40-20 (Ages as you go clockwise around the table) 2. The youngest person must be telling the truth, so the minimum is 1. Here is an example with 1 person telling the truth Seven people sit at a different round table, facing inwards, towards the centre of the table.
Each of them says “I am younger than the person to my left, and I am younger than the person two places to my right”. 3. At this table, what is the greatest possible number of people telling the truth? 4. At this table, what is the smallest possible number of people telling the truth? 3.
The two oldest people must be lying, so the answer cannot be six or seven. It turns out that the answer cannot be five either. If five were telling the truth, the third oldest would be one of them, and so the three oldest people would have to be arranged in one of the two cases below (suppose the ages are 10, 20, 30, 40, 50, 60, 70). * * * 60 * 50 70 (Ages as you go clockwise around the table) But now there is nowhere for the next oldest (the 40-year-old) to sit and be telling the truth.
It is, however, possible for four people to be telling the truth: 4. The youngest person must be telling the truth, so the answer cannot be zero. If you order everyone in descending order of ages, no one is telling the truth apart from the youngest: 999 people sit at a third round table, facing inwards, towards the centre of the table.
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