Question 4
a) Two soccer teams of ten players each play a match. One team consists entirely of truth-tellers, the other entirely of liars. Afterward, each player is asked how many goals he scored. Some answer “one”, Chau answers “two”, some answer “three”, and the rest answer “five”. Is Chau truthful or a liar, given that the truth-telling team wins 20–17?
b) Let $A=\overline{abcdef}$ be a six-digit number with $a\lt b\lt c\lt d\lt e\lt f$. Find the sum of the digits of $9A$.
b) Let $A=\overline{abcdef}$ be a six-digit number with $a\lt b\lt c\lt d\lt e\lt f$. Find the sum of the digits of $9A$.