Question 65
given an $m \times n$ table, each cell signed with "-". The following operations are
(i) to change all the signs in an entire row to the opposite, i.e. every "-" to "+", and every "+" to "-";
(ii) to change all the signs in an entire column to the opposite, i.e. every "-" to "+" and every "+" to "-".
a. Prove that if $m = n = 100$, using the above operations one cannot obtain 2004 signs "+".
b. If $m = 100$, find the least $n \gt 100$ for which 2004 signs "+" can be obtained.
(i) to change all the signs in an entire row to the opposite, i.e. every "-" to "+", and every "+" to "-";
(ii) to change all the signs in an entire column to the opposite, i.e. every "-" to "+" and every "+" to "-".
a. Prove that if $m = n = 100$, using the above operations one cannot obtain 2004 signs "+".
b. If $m = 100$, find the least $n \gt 100$ for which 2004 signs "+" can be obtained.