Natural numbers from
to
(not necessarily distinct) are written on
cards. It is given that the sum of the numbers on any subset of cards (including the set of all cards) is not divisible by
. Show that all the cards contain the same number.
%V0
Natural numbers from $1$ to $99$ (not necessarily distinct) are written on $99$ cards. It is given that the sum of the numbers on any subset of cards (including the set of all cards) is not divisible by $100$. Show that all the cards contain the same number.
Školjka