Answer:
1) There are 26 letters in the alphabet. Thus, 27 people must be chosen because otherwise there could be 1 person per initial.
2) There are 7 days in a week. Thus, if the first 7 had their birthdays on every day of the week, the 8th person must share a birthday on the same day of the week as another.
3) A phone number can contain 0,1,2,3,4,5,6,7,8,9. Thus, if the first 10 people have a phone number that ends with each digit, the 11th must share it, as there are no unique options.
4) 100/2 = 50. Thus, the minimum each bag could have is 50.
5) 19/3 > 6. The maximum number you could get with numbers less than seven is 6,6,6 = 18. 18<19. Thus, you need a number 7 or greater.
6) The worst scenario that could happen here is that you grab 8 German books, 10 French books, and 12 Spanish, Russian and Italian books. This would be 54 books. Thus, with the 55th book, you must have gotten 12 of at least one subject. Thus, the answer is 55 books.
7) This is vague. If she cannot repeat any of the three jokes in the triplet, then she must have 36 jokes for this to be possible, because 12*3=36
8) Each of the remaining 29 students made less than 12 mistakes. Even if 2 students made 11,10,9,8,7,6,5,4,3,2,1 mistakes, there would still be multiple students left that would have made 11,10,9,8,7,6,5,4,3,2, or 1 mistake(s), meaning that at least 3 students made the same amount of mistakes.
9) 465/95 = about 4.9. Thus, each table could have less than 6 seats, so we cannot be sure.
Hope it helps <3
