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59
REFLECTIONS
ON THE WAY TO SCHOOL
- Vavtobus
The Indian bus without a conductor included 15 independent people. None of them have copper children, but only coins in denominations of 10, 15 and 20 kopecks. (A ticket costs 5 kopecks. You can throw any coin into the ticket office and tear off the corresponding number of tickets.) Nevertheless, the passengers who entered were able to pay for the fare by taking change from each other. Think about how this could be?
For those who have solved this problem, we suggest solving three more difficult ones:
- Prove that these passengers had at least 20 silver coins (otherwise they would not have been able to pay).
- Prove that they had at least eight 15-point coins.
- Prove that all passengers together had at least 2 rubles. 50 k.
Of course, it is possible to come up with an example where N passengers pay only with coins in denominations of 10, 15, 20 kopecks for any N≥2. Think about what the exact and estimates are for the total number of coins, the total number of coins and the total number of coins in this case? N.V.