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MathNet 2017-part-04 — 176 problems (EN–VI) Question 97

Math Olympiad Vault · MathNet 2017-part-04 — 176 problems (EN–VI)

Question 97

The boat is sinking! Passengers must then be saved, but the rescuer must know their count. If the passengers group themselves into $7$, one group will only have $4$ passengers. If the passengers group themselves into $11$, one group will only have $7$ passengers. If the passengers group themselves into $13$, one group will only have $10$ passengers. How many passengers are there if the boat carried at most $1000$ passengers?