self Maths Puzzle

20 passengers are in a sinking ship. 10 are mathematicians. They all stand in a ring. Every 7th climbs into the lifeboat which can only hold 10 people. Where should the mathematicians stand in the ring?

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self Other Question

12 black mice and 1 white mouse are in a ring. Where should a cat start so that if he eats every 13th mouse the white mouse will be last? 30 passengers are in a sinking ship. They all stand in a circle. Every 9th passenger goes overboard. The lifeboat holds 15. Where are the 15 lucky positions in the circle?