In a certain land live dwarves; any two of them either are friends or hate each other. It is known that there are no three dwarves who all hate each other. Must there necessarily exist three dwarves who are all pairwise friends if in this land there are (A) \(5\) dwarves, (B) \(6\) dwarves?

Kādā zemē dzīvo rūķi, katri divi no tiem vai nu draudzējas, vai viens otru ienīst. Zināms, ka nav tādu trīs rūḳu, kas visi viens otru ienīst. Vai noteikti var atrast tādus trīs rūḳus, kas visi savā starpā draudzējas, ja šajā zemē ir (A) \(5\) rūķi, (B) \(6\) rūķi?