Question 5
Anna and Boris play a game using the integers $1,2,3,4,5,6,7,8$. Anna first selects a positive integer $k\le8$. Boris then chooses $k$ of these eight numbers, and Anna chooses three of the eight numbers. Anna wins if the sum of every pair of her chosen numbers is among the numbers chosen by Boris.
(a) What is the minimum value of $k$ for which Anna has a winning strategy? (2 marks)
(b) If Anna has a winning strategy for $k$, give a counterexample showing that for $k-1$ she cannot guarantee a win. (4 marks)
Answer-sheet instruction: no partial score for each subpart.
(a) What is the minimum value of $k$ for which Anna has a winning strategy? (2 marks)
(b) If Anna has a winning strategy for $k$, give a counterexample showing that for $k-1$ she cannot guarantee a win. (4 marks)
Answer-sheet instruction: no partial score for each subpart.