3rd and 4th Grade, February, 2019

    A.1233. Olga’s dad is building a fence around their rectangular shape garden. One side of the garden is three times as long as another side. He used three times as much chicken wire (672 meters more) than he needed. When he realized that he fenced in the gate as well, he said: “Oops! Nobody in and nobody out!” How long are the sides of this garden?

    A.1234. An amateur number magician wrote all the even numbers from 10 to 32 one-by-one on 12 discs. After a few fancy moves and spells, he promised to have 6 discs in one hat and six discs in another hat so that the sums of the numbers on the discs in each hat are the same. Unfortunately for him, the sums were 20 apart.

    a) What kinds of discs could be in each hat now?

    b) What kinds of arrangements of the discs would have been correct?

    A.1235. Last Spring in Newlands County Johnny Counter placed house numbers on each of the 100 houses on New Street. One side is numbered with even numbers and the other side with odd numbers. There are 60 houses on the odd side and 40 houses on the even side of the street. He started with 1 on the odd side, then 2 on the even side, alternating each time between the sides using the correct numbers in an increasing order. Once he put up the digits 4 and 7 on the house with number 47, he realized that he ran out of the digit 7’s. “It does not matter to me” – he said, ” I will use 2 for every 7 from now on, I have enough 2’s.” And so he did, he used a digit 2 for every digit 7 from then on.

    a) How many houses received the wrong house number?

    b) How many digit 2’s did Johnny use up all together?

    A.1236. In the school library the librarians placed the books for the lower school children on 4 shelves, 162 books on each shelf. 98 out of them are collections of poems, twice as many are fairy tales, 56 more than that are books on sports, and the rest are novels. How many of the books are novels?

    A.1237. Fiona read 3 of the 6 books her teacher recommended to her summer reading. One of them was Winnie the Pooh. How many different choices did she have?

    A.1238. What number goes in place of the question mark and why?

    3 (32) 11

    27 (16) 31

    83 ( ? ) 88

    A.1239. The school library is open on Mondays from 12:00 – 12:45, on Tuesdays from 14:00 – 15:35, on Wednesdays from 13:00 – 14:00, on Thursdays from 13:00 – 13:45, and on Fridays from 12:00 – 13:15. The librarians divided the weekly opening time equally among the lower school classes from (1st through 4th grades). How many minutes of library time do the second graders have in a week?

    A.1240. The publisher used 387 digits to number the pages of a children’s book by starting the numbering on the 7th page. How many pages does this book contain?

    Please send your solutions here.

    The Sharma Kamala Educational Trust is sponsoring the participation of students from India. So, if you are a student living in India, please, send your solutions to: Group A from India

    Back to Paul Erdős International Math Challenge

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