3rd and 4th Grade, March, 2020

    A.1297. The Giant Panda is an endangered species. Only about 3000 of them live in the wild in China. They mostly eat bamboo shoots. Four pandas are able to eat 288 kg of bamboo shoots in 6 days. With a similar diet,

    a) How many kilograms of bamboo shoots can 10 pandas eat in 12 days?

    b) How many pandas can eat 5760 kg of bamboo shoots in 30 days?

    c) How many days does it take 3 pandas to eat 288 kg of bamboo shoots?

    A.1298. The Galago, also known as the Little Night Monkey, may search 200 to 300 trees a night for its main diet of gum, nectar, and insects. How many trees did the Galago visit last night if he found gum on 139 trees, insects on 88 trees, nectar on 109 trees, gum and nectar on 61 trees, nectar and insects on 17 trees, gum and insects on 28 trees? 5 trees had all three: gum, nectar and insects on them. He did not visit any tree that he could not find any food on.

    A.1299. The king’s palace has 4 floors. There are 15 rooms on each floor, and 6 windows in each room. For decoration, there are two statues in every other window, and every fifth statue is made out of marble, the rest of them are made out of granite. How many granite statues are there in the palace?

    A.1300. Princess Jewels has a total of 124 necklaces and wristbands. She has 16 more necklaces than wristbands. One day she gave half of her necklaces and a third of her wristbands to her girlfriend, Princess Helena, from the neighboring kingdom, as a present. How many necklaces and how many wristbands did Helena receive?

    A.1301. When I was 8 years old my father was 31. Now he is twice as old as I am. How old I am?

    A.1302. Is the sum of the first 100 prime numbers even or odd?

    A.1303. We wrote the numbers 1, 2, 3, … , 11 on separate sheets of paper, one number on every sheet. We mixed them and separated them into two boxes. Andy added the numbers in one of the boxes, and Bea did the same thing with the other box. Then Bea said:

    “Interesting! My number is six times as big as Andy’s.”

    Is this possible?

    A.1304. In an office the boss puts a letter on his secretary’s desk at different times of the day for her to type it up. He always gives one letter at a time and always puts it on top of the other letters that were already on the desk. The secretary, when she has time, takes a letter from the top of the pile and types it up. If there are 5 letters, and the boss put them down in the 1-2-3-4-5 order, in which of the following orders is it impossible for the secretary to type these letters?

    A) 1-2-3-4-5

    B) 2-4-3-5-1

    C) 3-2-4-1-5

    D) 4-5-2-3-1

    E) 5-4-3-2-1

    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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