1.3. Rex, Dzhulbars, Tarzan, Barbos and Sharik are frolicking on the lawn. Rex has bitten the one who has bitten Dzhulbars, Dzhulbars - the one who has bitten Tarzan, Tarzan - the one who has bitten Barbos, Barbos - the one who has bitten Sharik, Sharik - the one who has bitten Rex. Who, then, has bitten Rex?

## Second Round
## 1.3. Answer: Tarzan.

Solution 1. Suppose Rex was bitten by Dzhulbars. Then Sharik bit Dzhulbars, and Rex bit Sharik. But then Tarzan and Barbos would have bitten each other, which is impossible. Similarly, other possibilities are checked, and it is established that if Tarzan bit Rex, and Rex, Dzhulbars, Barboss, and Sharik bit Barboss, Sharik, Dzhulbars, and Tarzan respectively, then all conditions will be met.

![](https://cdn.mathpix.com/cropped/2024_06_04_7a3ed3d68324df2727b5g-13.jpg?height=988&width=953&top_left_y=74&top_left_x=560)

Fig. 4: to the solution of problem 3.2

Solution 2. Let's denote the dogs as points and the biting as arrows. Then the dogs are divided into cycles. If we enlarge the step, moving along a pair of adjacent arrows, we will end up with one cycle. Its length is 5 and Rex is on this cycle. We know what happens one step away from each dog, so the cycle is uniquely determined.

## Second Round