5th and 6th Grade, September

    B.1193. Olga has a bag of balls, 10 of them are red, and the other 12 are white. She pulls a ball out of the bag. If it is red, she puts it back and puts another 5 red balls into the bag. If it is white, she puts it back and she puts 3 more white balls into the bag. When, after putting the balls into the bag, she has exactly 43 balls in the bag, she stops. How many red and how many white balls does she need to pull for this to happen?

    B.1194. Your digital clock shows the time from 00:00 till 23:59. At 5 minutes passed 3 o’clock in the afternoon you see 15:05 showing on your clock. If you consider this to be a division then the quotient is 3 and the remainder is zero. How many such times are there in a day when the “quotient” is a whole number and the remainder is zero?

    B.1195. You may use two kinds of square shaped tiles: the sides of the red tiles are 20 cm, the sides of the blue tiles are 10 cm. Using a total of 6 tiles, make a bigger square. How many blue tiles are needed to cover this bigger square?

    B.1196. You have 64 identical red cubes. You paint one of them blue, and then you make a 4x4x4 cube using all 64 of them. How many different cubes can you possibly make if those big cubes that can be rotated into the same position are not considered to be different?

    B.1197. Write down every 2-digit number in an increasing order in one line by using red, blue and green colors continually in this order for every digit. Did you have to write every digit in every color?

    B.1198. On the diagram, below the perimeters of the identical rectangles are 16 cm, and the area of the small square in the middle is 16 square centimeters. How big is the area of each of the identical rectangles?

    B.1199. In how many 4-digit numbers is the sum of the digits 5?

    B.1200. Divide the numbers 2, 3, 4, and 5 into two groups of two numbers so that the sum of the products of the numbers in each group is the smallest possible number.

    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 B from India

    Back to Paul Erdős International Math Challenge


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