18.80 A $8 \times 10$ table, as shown in Figure (1), is placed in the corner of a square room. The owner of the house wants to move the table to the position shown in Figure (2).

If the side length of the room is $S$, then to make the move possible without tilting the table or cutting it, the minimum integer value of $S$ is
(A) 11.
(B) 12.
(C) 13.
(D) 14.
(E) 15.
(39th American High School Mathematics Examination, 1988)
[Sol] Since if the rectangular table is moved from vertical to horizontal, the narrowest part of the room should allow the diagonal of the table to move (change direction).
$\because \quad \sqrt{10^{2}+8^{2}}$ is not an integer,
$\therefore \quad S_{\min }=\left[\sqrt{10^{2}+8^{2}}\right]+1=[\sqrt{164}]+1=13$.
Therefore, the answer is $(C)$.