Question 120
Tokens are placed in some of the cells of a table of size $8 \times 8$ such that:
(1) there is at least one token in any rectangle of size $2 \times 1$ and $1 \times 2$;
(2) there are two neighboring tokens in any rectangle of size $7 \times 1$ and $1 \times 7$.
Find the minimum possible number of tokens.
(1) there is at least one token in any rectangle of size $2 \times 1$ and $1 \times 2$;
(2) there are two neighboring tokens in any rectangle of size $7 \times 1$ and $1 \times 7$.
Find the minimum possible number of tokens.