Question 18
Some knights are on a playground. Each knight has three properties: speed, smartness and sightliness. For every knight, each property takes a certain integral value $x$ such that $1 \le x \le n$. A knight $A$ can win a knight $B$ if the speed, smartness and sightliness of $A$ are all greater than those of $B$. It is known that none among the knights on the playground can win any of the other knights and every two knights differ by at least one property. Find the largest possible number of knights on the playground.