Can you solve it? The treacherous riddle of the round table

It’s made of wood, it’s in the shape of a circle, and it is the forum for many an important gathering.

It is also the setting for today’s puzzle.

The round table

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?

Seven people sit at a different 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, 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?

999 people sit at a third 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 three places to my left, and older than the person three places to my right”.

5. At this table, what is the greatest possible number of people telling the truth?

6. At this table, what is the smallest possible number of people telling the truth?

I’ll be back at 5pm UK with the solutions.

PLEASE NO SPOILERS. Instead please discuss round tables.

Thanks to Daniel Griller, a longtime friend of this column, who wrote today’s puzzles. He is the author of the excellent puzzle books Elastic Numbers and A Ring of Cats and Dogs, and Other Curious Puzzles.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.