**K. 109.** In a football championship, Peter's favourite team scored a total of three goals in the first four matches played. Other teams scored a total of two goals against the team. Given that a team gets 3 points for winning, 1 for a draw and none if they lose the game, how many points may Peter's favourite team have after the four matches played?

(6 points)

This problem is for grade 9 students only.

**K. 110.** In Dragon Castle, 14-headed baby dragon is sleeping while mummy dragon is making pancakes. She lays them on a plate and leaves home. One head wakes up, eats 1/11 of the pancakes and falls asleep again. Then another head wakes up, eats 1/13 of the remaining pancakes and falls asleep again. Next, three heads wake up at the same time, eat 1/14 of the pancakes each, and finally they wake up the rest of the heads, too. Those who have eaten, do not get any more pancakes, the remaining 9 heads eat them all. (They do not necessarily eat the same number.) How many pancakes may have been on the plate, given that every head ate a whole number of pancakes, and if they had shared them equally, no one would have got more than 143?

(6 points)

This problem is for grade 9 students only.

**K. 111.** In a game, two dice are rolled and there are 9 cards numbered 1 to 9. The total of the numbers rolled is to be put together as a sum of number cards (or a single card). Each card can only be used once. Used cards are set aside and the sum of the next two numbers rolled is put together out of the remaining cards. And so on while it is possible.

*a*) What is the minimum number of rolls may in a sequence of rolls where all number cards are used up? Give an example, too.

*b*) In the worst case, what is the smallest number of rolls that may end the game?

(6 points)

This problem is for grade 9 students only.

**K. 114.** Steve has three classmates named Smith, four named Black, one named White and two named Tailor. Among these boys, there are four with the first name of Jack, two called Alex, three called Bob and one Martin. Each boy has only one first name, and no two boys in the class have exactly the same name. What are the full names of these classmates of Steve?

(6 points)

This problem is for grade 9 students only.