3rd and 4th Grade, December, 2018

    A.1217. The children set up 8 tents in their summer bird-watching camp as shown on the diagram below. The 28 children moved into their tents in such a way so that in the 3 tents on any side of the camp there were a total of 10 children.

    a) How many children could stay in each tent?

    b) Two children had to go home in the middle of the week. Again, the children re-arranged themselves in the tents so that in the 3 tents on any side of the camp there were a total of 10 children, still. How many children could stay in each tent now?

    A.1218. For ringing them, the children could capture 4 different kinds of birds in the first week of camp. They captured 3 less finches than sparrows, and 4 times as many cardinals as finches. The 8 sparrows captured was 2 more than a third of bluebirds. How many birds did the students capture that week?

    A.1219. There was a watch tower next to Tom’s tent. A snail started to climb up on it at 8:00 am. Every hour it climbed 80 cm in 45 minutes, then rested for 15 minutes while it slid back down 20 cm. At 4:00 pm the children saw the snail on the top of the tower. What is the maximum possible height the tower could be?

    A.1220. There are 3 trails by the camp with a total length of 4540 m. The trail of the herbs is 620 m shorter than the trail of the hidden treasures. The trail of rocks is 1260 m long. How much did the children walk yesterday if they hiked the trail of rocks and the trail of the hidden treasures from beginning to end?

    A.1221. In a nearby cave 3 kinds of bats live: 5 fruit bats, 2 spotted bats, and 4 bumblebee bats. Three of them fly out of the cave. What is true for sure about the bats remaining in the cave?

    a) None of them is a bumblebee bat.

    b) There is at least one bumblebee bat amongst them.

    c) All of them are fruit bats.

    d) There is no more spotted bat left in the cave.

    e) There is at least one of every kind of bat.

    f) There are two fruit bats left in the cave.

    A.1222. Olga is collecting stickers. From three of her friends, Maria, Beatrix and Petra, she received a total of 6 identical stickers. How many different ways could Olga receive these 6 stickers if each of her 3 friends gave her at least one sticker?

    A.1223. Amaya is a napkin collector. She brought her two most beautiful kinds of napkins (animal motives and flower motives) to the fair to sell them. Two animal motive napkins cost the same as five flower motive napkins. Six animal motive napkins cost $1.50. How much do one flower and one animal motive napkin cost together?

    A.1224. Arshaan loves to make model airplanes and model motorcycles. One day he wanted to show some of them to his class. He did not take 8 airplane models and half of his motorcycle models to school, so he left 26 models at home. He has three times as many motorcycle models as airplane models. How many motorcycle and how many airplane models does Ben have?

    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, December, 2018