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## Main Question or Discussion Point

Hi - My first post here and was looking for some help with this problem.

Not sure where to start so hope some pointers would get me going/thinking!

Q:

Suppose that there is a party with n ≥ 2 people and that each person gives presents to one or more people at the party (but no more than one present to any single person). Are the following true or false? Give a proof or a counterexample as appropriate:

a) There are at least two people at the party who receive the same number of presents.

b) There are at least two people at the party who give the same number of presents.

c) It is not possible to have a party where everybody gives more presents than they receive.

Thanks for the advice in advance,

Felix

Not sure where to start so hope some pointers would get me going/thinking!

Q:

Suppose that there is a party with n ≥ 2 people and that each person gives presents to one or more people at the party (but no more than one present to any single person). Are the following true or false? Give a proof or a counterexample as appropriate:

a) There are at least two people at the party who receive the same number of presents.

b) There are at least two people at the party who give the same number of presents.

c) It is not possible to have a party where everybody gives more presents than they receive.

Thanks for the advice in advance,

Felix