The problems are not well designed. Some of them are extremely demanding and some of them are with mistakes.
I will try to maintain a list of unofficial errata and notices here.
Chapter 7, Problem 11 (a): The hint is misleading, ignore it.
Chapter 7 Problem 14: A compulsory condition must be added -- \(p(x)\) need to be uniform. Or, more generally, to select an \(x\) that maximises \(p(x, y)\) for each \(y\), NOT the conditional probability. The second sub-problem is meaningless. It is always not true if \(\mathcal|Y| < \mathcal|X| \).