Problem 4. Joseph solved 6 problems correctly, Darko solved 5 problems incorrectly, and Petre had the same number of correct and incorrect solutions. How many problems did all three solve correctly together, if Joseph solved twice as many problems correctly as Darko?
Solution. Darko definitely solved half of the problems given by Josif, which means he solved $6: 2=3$ problems. Since Darko had 3 correct and 5 incorrect problems, the test had $3+5=8$ problems. Petre correctly solved half of the problems, which means he had 4 correct solutions. Finally, all together they correctly solved $6+3+4=13$ problems.