欢迎大家: 八月 2023

2023年8月9日星期三

2022 AMC 10A P12&P13

P12 On Halloween children walked into the principal's office asking for candy. They can be classified into three types: Some always lie; some always tell the truth; and some alternately lie and tell the truth. The alternaters arbitrarily choose their first response, either a lie or the truth, but each subsequent statement has the opposite truth value from its predecessor. The principal asked everyone the same three questions in this order.

"Are you a truth-teller?" The principal gave a piece of candy to each of the children who answered yes.

"Are you an alternater?" The principal gave a piece of candy to each of the children who answered yes.

"Are you a liar?" The principal gave a piece of candy to each of the children who answered yes.

How many pieces of candy in all did the principal give to the children who always tell the truth?

P13 Let $\triangle ABC$ be a scalene triangle. Point lies on $\overline{BC}$ so that $\overline{AP}$ bisects $\angle BAC.$ The line through perpendicular to $\overline{AP}$ intersects the line through parallel to $\overline{BC}$ at point Suppose and What is