12
Part of 2022 AMC 10
Problems(2)
Halloween Candy
Source: 2022 AMC 10A #12 / 2022 AMC 12A #9
11/11/2022
On Halloween 31 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 22 children who answered yes."Are you an alternater?" The principal gave a piece of candy to each of the 15 children who answered yes."Are you a liar?" The principal gave a piece of candy to each of the 9 children who answered yes.How many pieces of candy in all did the principal give to the children who always tell the truth?
AMCAMC 10AMC 122022 AMC2022 AMC 10a2022 AMC 12Alogic
Sum of dice is 7
Source: 2022 AMC 10B P12
11/17/2022
A pair of fair -sided dice is rolled times. What is the least value of such that the probability that the sum of the numbers face up on a roll equals at least once is greater than ?
probabilityAMCAMC 102022 AMC2022 AMC 10BDice