Školjka Let 
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
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.
b.
c.
Justify your answer(s).
[For example, when n=4, Alice may choose the numbers 1, 5, 7, 9, which have the same pairwise sums as the numbers 2, 4, 6, 10, and hence Bob cannot be sure to win.]
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
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.
b.
c.
Justify your answer(s).
[For example, when n=4, Alice may choose the numbers 1, 5, 7, 9, which have the same pairwise sums as the numbers 2, 4, 6, 10, and hence Bob cannot be sure to win.]