Problem 4.3. All seats at King Arthur's round table are numbered clockwise. The distances between adjacent seats are the same.

One day, King Arthur sat at seat number 10, and Sir Lancelot sat directly opposite him at seat number 29. How many seats are there in total at the round table?
Answer: 38.

Solution. Along one side of the table between Arthur and Lancelot are seats numbered $11,12, \ldots, 28$ - a total of exactly 18 seats. Since these two are sitting directly opposite each other, there are also 18 seats on the other side of the table. Therefore, the total number of seats at the table is $18+18+1+1=38$.