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MathNet 2015-part-01 — 191 problems (EN–VI) Question 126

Math Olympiad Vault · MathNet 2015-part-01 — 191 problems (EN–VI)

Question 126

Pedro decided to take all his children, boys and girls, to have ice cream at the ice cream shop Sorvete Matemático. At the shop there are 12 different flavors of ice cream and each child ordered a combo with 3 scoops of ice cream. After leaving the shop, Pedro realized that, in total, exactly two scoops of each flavor available at the shop had been ordered.

a) Knowing that Pedro did not eat ice cream, what is the total number of his children (girls and boys)?

b) Pedro looked more carefully at the flavors each one ordered and noticed that no flavor was ordered by both a boy and a girl, that is, if a boy chose a flavor, no girl chose that same flavor. Knowing that at least one of his children is a boy and that he has more daughters than sons, determine the number of his daughters.