Question 18
Let $n$ be a positive integer. Two players, Alice and Bob, are playing the following game:
* Alice chooses $n$ real numbers, not necessarily distinct
* Alice writes all pairwise sums on a sheet of paper and gives it to Bob (there are $\frac{n(n-1)}{2}$ such sums, not necessarily distinct)
* Bob wins if he finds correctly the initial $n$ numbers chosen by Alice with only one guess.
Can Bob be sure to win for the following cases?
a. $n=5$
b. $n=6$
c. $n=8$
Justify your answer(s).
* Alice chooses $n$ real numbers, not necessarily distinct
* Alice writes all pairwise sums on a sheet of paper and gives it to Bob (there are $\frac{n(n-1)}{2}$ such sums, not necessarily distinct)
* Bob wins if he finds correctly the initial $n$ numbers chosen by Alice with only one guess.
Can Bob be sure to win for the following cases?
a. $n=5$
b. $n=6$
c. $n=8$
Justify your answer(s).