3rd and 4th Grade, December, 2019

    A.1273. Basilisk lizards are unique because they can run across the surface of water. (See it on: http://www.youtube.com/watch?v=_ut5jENqBX8) It can even run 10 meters in 4 seconds. The females lay 12 to 14 eggs 5 times a year.

    a) How far can this lizard run on water in a half a minute?

    b) At most how many eggs can hatch from 6 females in 2 years?

    A.1274. The American Coot, to save her eggs from predators, sometimes builds a nest from rocks in the middle of a shallow lake. They carry the stones, which are about 30 dkg in mass, with their beaks. The male carries about 3000 stones to build the nest, which is about one and a half times more than what the female can carry. What is the mass of all the stones a couple of American Coots carry to build a nest?

    A.1275. The Kalong, also known as the Flying Fox, has a wingspan of almost 1.5 meters for a body length of 40 centimeters, so its wings are comparable to those of a large bird of prey. Just like bats, they sleep hanging upside down, holding onto the horizontal branches of a tree. On the lower branches there are 4 times as many kalongs as on the middle branches. On the upper branches there are 4 more kalongs than on the middle branches. How many kalongs are there on the lower branches of this tree if there are a total of 112 kalongs on the tree?

    A.1276. How many different 4-digit numbers can you create by using two 1’s, a 2, and a 3?

    A.1277. The Arctic Tern, a seabird, is the champion of long-distance flying. They see two summers each year as they migrate from the North Pole, along a winding route to Antarctica and back, a round trip of about 70,000 km (44,000 miles) each year. They spend about 14 weeks at each pole, the rest of the year they spend flying.

    a) How long does it take them to fly from one pole of the Earth to the other?

    b) The lifespan of an Arctic Tern is 20 years. How much of it does this bird spend with migrating?

    A.1278. Olga made a paper cube for her math class. She wrote on each side how many other sides it borders with, she wrote by every edge how many vertices it connects, and she wrote at every vertex how many edges run into it. What is the sum of all these numbers on the cube?

    A.1279. Inga drew all the diagonals of a regular pentagon. How many triangles of different shapes are there on the picture?

    A.1280. Anna wants to write the numbers from 0 to 9 on the circumference of a circle so that the sum of any three consecutive numbers on the circle is no more than 15. Is it possible to do?

    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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