## 3rd and 4th Grade, March, 2019

A.1241. The Book of Little Magicians contains 45 pages. When numbering its pages they used only even digits. (For example: the number on the 3rd page is 6. ) What number is on the last, the 45th, page? Which page has the number 204 on it?

A.1242. There are a total of 5400 books in the 2 reading rooms of a library. If the librarian took a quarter of the books and 36 more from one of the rooms to the other, both rooms would have an equal number of books in them. How many books are there in each of the rooms now?

A.1243. In a school there are four homerooms in the 4th grade: A, B, C, and D. Yesterday, there was a swimming competition between these homerooms. This morning I heard the following comments about the competition:

– Homeroom A did not win the competition.

– Homeroom D finished behind homeroom B.

– Homeroom B did not finish in 2nd place.

– Homeroom D finished ahead of homeroom A.

What was the result of the competition?

A.1244. There were 16 pairs competing in a dance competition. After 2 minutes the judges asked 3 pairs to leave the competition. A half a minute later they started dancing again, but 2 minutes later the judges asked another 2 pairs to leave the floor. A half a minute later the remaining pairs started dancing again, and from then on the judges asked only one pair to leave after every 2 minutes of dancing, each time the dancing stopped for a half a minute. Finally, the winners danced for 5 minutes. How long did this competition go on?

A.1245. How many different ways can you write 100 as the sum of 2 primes?

A.1246. In a soccer league every team played every team exactly once. Here are the scores:

a-b:2-4, a-c:1-0, a-d:3-3, b-c:3-3, b-d:2-0, c-d:2-2

For every win a team gets 3 points, for a tie each team gets 2 points, for a loss a team gets 1 point.

a) What was the final standing? (In case of equal points between two team, you have to look at their score against each other, and if that also was a tie, then the better goal differential (goals scored minus goals received) decides the order.

b) Which team scored the most goals?

A.1247. In a calculating competition the winner, Abigail, calculated only 3 problems incorrectly:

– First she calculated the 8th problem incorrectly as she got 59, which is 2 more than three times the correct answer.

– In the 14th problem, she added 25 instead of 250, and subtracted 200 instead of 20, and that is how she got 400.

– In the 42nd problem, she added 6×8 and subtracted 9×7 (instead of the other way around), and so she got 620.

What were the correct answers of these three problems?

A.1248. In a school competition every team had to answer 20 questions. The judges gave 5 points for every correct answer, but deducted 2 points for every incorrect answer. They deducted 2 points even if a team did not answer a question. How many correct answers did the following teams give if their points were as follows:

Team A: 44 points, Team B: 86 points, Team C: 65 points, Team D: 72 points