3rd and 4th Grade, November, 2018

    A.1209. Olga and Oliver decided that they are going to play an instrumental music duo for their class. They both could choose from the following instruments: drum, recorder, xylophone, or piano. How many different ways can they play music for the class if they do not play on the same instrument on the same piece?

    A.1210. During a Physical Education class 12 girls and 10 boys created two different circles. They were throwing a ball around their circle always in the same direction, always skipping the same (at least one) number of children. How many children can they skip in each group if they do not want to leave anybody in the group out of the game?

    A.1211. Using the digits 1, 2, 3, 4, and 5, fill in the blank fields in the 5×5 grid below so that each row and each column would have one of each digit in it. What is the product of the numbers in the fields marked by question marks?

    A.1212. In a Literature class the teacher asked his students how much they had already read of the next book they were going to discuss.

    “I have read 2/3 of the book already.” – said Peter.

    “I have read 120 less pages than Peter, and this is only a quarter of what Peter has read.” – said Paul.

    How many pages are there in this book, and how many pages has each of the boys read?

    A.1213. In their Drawing class Fiona’s group created invitation cards decorated by 5-petal flowers. They colored the petals using three warm colors: red, orange, and purple; and two cold colors: blue and green. For every flower they used a warm and a cold color. How many different flowers could they put on the invitations if every petal is colored by only one color? (Two flowers are considered to be the same if you can rotate one into the other.)

    A.1214. In a Math class the children made several 3cmx3cmx3cm cubes. They then made different solids, using 4 of them at a time and gluing them together on perfectly aligned faces. (Two solids were considered to be the same if one looked the same as another after a rotation and/or reflection.) How many different solids did they create?

    A.1215. A group of children goes on a bird catching trip. They want to observe how the birds migrate so they wanted to put marking rings on the legs of the birds. So on Monday morning they set up 4 bird catching nets. Olivia’s is 26 decimeters 50 centimeters long, Anna’s is 4 meters 7 decimeters long, Sue’s is 11 meters 50 centimeters long, and Tom’s is 500 centimeters long.

    a) How much longer is the longest net than the shortest one?

    b) What is the total length of the 4 nets?

    A.1216. Last weekend, with her family, Anne went on a hike in the forest. On a rotting tree 6-legged Giant Hunting Ants and Wasp Spiders were running all over. Anne counted 5 more spiders than ants, and a total of 82 legs. How many spiders and how many ants were there on the tree?

    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

    Posted in Uncategorized | Comments Off on 3rd and 4th Grade, November, 2018