3rd and 4th Grade, November, 2019

    A.1265. Five teams participated in a soccer league. Each team played against every team exactly once. Due to a tie for first place they had to play one more game. How many games did the teams play in total in this league?

    A.1266. Every morning Yuria, Christie, and Rebecca go horseback riding. They each choose from four beautiful horses, Lightening, Dew, Star and Moon. How many different ways can the girls ride? Two ways count as different if at least one girl is on a different horse.

    A.1267. Last afternoon there was a strong wind, so Mark, Eve and Adam decided to fly their kites. Mark’s kite went 8 meters higher than Eve’s and stayed in the air for 3/4 of an hour, 3 minutes longer than Adam’s. Adam’s kite flew twice as high as Mark’s, and Eve’s kite went up to 38 meters but stayed in the air for 8 minutes less than Adam’s. How high did these kites go up and how long did they stay in the air?

    A.1268. Marlon set up an obstacle course for a race. He marked the path by using twelve 2-meter long, eight 5-meter long, and nine 3-meter long poles that he laid down back to back without any gaps in between the poles. Later he decided to shorten the course a little, so he took out 2 poles. How long could the shorter course be now? (List all the options!)

    A.1269. A class split into two groups on a hiking trip. One group started the hike from the lookout point at the top of the mountain, while the other group started from a hunters’ hut, 12 km from the lookout point. The two groups started hiking toward each other at the same time on the same trail. The group starting from the hunters’ hut going upwards made 50 meters every minute, while the other group going downhill made 70 meters every minute.

    a) What time did the two groups meet if they left at 3:00 pm, and they both took a 15-minute break before they met?

    b) How far were they from the lookout point when they met?

    A.1270. The first section, a ninth of a 36-kilometer bicycle tour, was a sandy road. The next section, a sixth of the tour, was on asphalt, then 2 km on a dirt road. A quarter of the remaining part of the tour was a pebble road, and the remainder a forest trail. The first checkpoint was at the start, and then there was one every 3 km.

    a) How long was the section in the forest?

    b) What kind of road was the sixth check point on?

    A.1271. One of the mammals with the longest winter hibernation is the Hazel Dormouse. It sleeps through more than half of its lifetime, for 7 months a year. How many weeks has a 4-year-old Hazel Dormouse slept in its lifetime?

    A.1272. The little Hazel Dormouse awakes from its long winter sleep around May very quickly. Its cold body warms up very fast. In the first quarter of an hour its body temperature rises 3 degrees Celsius every 5 minutes, in the second quarter of an hour it rises by 4 degrees Celsius every 5 minutes, in the third quarter of an hour it warms up another 9 degrees Celsius and reaches the normal 36 degrees Celsius. How low is the body temperature of the Hazel Dormouse during its winter hibernation?

    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, 2019