Step 1: Understanding the Argument.
The passage argues that the self-portrait cannot be from 1930. Why? Because in 1930 Brandon was 63 years old, but the painting shows a much younger man.
So, the reasoning assumes something: if Brandon was 63, he would not have painted himself looking young.
Step 2: Analyzing the Options.
- (A) Talks about the existence of other portraits but doesn’t address the reasoning of this argument.
- (B) Talks about Brandon’s intentions in not dating his works — irrelevant to the argument.
- (C) Talks about literature available — again irrelevant.
- (D) Directly supports the reasoning. If we assume Brandon would not have painted himself looking younger when he was actually 63, then the conclusion that the dating is wrong follows logically.
- (E) This only says he painted himself older at times, but does not rule out the possibility of painting himself younger too.
Step 3: Conclusion.
The assumption needed is that Brandon, when 63, would not have painted himself as a young man. This ensures the dating to 1930 is wrong. Hence, the correct answer is:
\[ \boxed{\text{(D) Brandon at age 63 would not have portrayed himself as a young man.}} \]

Two players \( A \) and \( B \) are playing a game. Player \( A \) has two available actions \( a_1 \) and \( a_2 \). Player \( B \) has two available actions \( b_1 \) and \( b_2 \). The payoff matrix arising from their actions is presented below:

Let \( p \) be the probability that player \( A \) plays action \( a_1 \) in the mixed strategy Nash equilibrium of the game.
Then the value of p is (round off to one decimal place).
Three friends, P, Q, and R, are solving a puzzle with statements:
(i) If P is a knight, Q is a knave.
(ii) If Q is a knight, R is a spy.
(iii) If R is a knight, P is a knave. Knights always tell the truth, knaves always lie, and spies sometimes tell the truth. If each friend is either a knight, knave, or spy, who is the knight?