Least and Most( Week 16 Evaluation) 1. There are 40 balls of 4 different colors in a bag. There are an equal number of balls for each color. At least how many balls need to be taken out from the bag so that there are 3 balls which are the same color? 2. If humans have up to 160,000 hairs, at least how many people will have same number (including zero) of hair(s) with someone else in a city with a population of 210,000 people? 5. A bag contains 220 beads. All the beads are the same, but in 4 different colors. There are equal number of beads for each color. If Emily is blindfolded and picks beads from the bag, what is the fewest number of beads she has to pick in order to be absolutely sure that there are 14 beads of the same color? 6. A bag contains 553 beads. All beads are the same shape, size, and in one of 7 colors. The number of beads is the same for each color. If David picks the beads blindfolded, at least how many beads will David need to pick to make sure that there are at least one bead of each color among the beads that he has picked? 7. From the natural numbers 1 to 82, at least how many numbers need to be picked to make sure that there is at least one number which is a multiple of 6? 8. Andy and Larry want to pay their membership fee in a MODEL club. The membership fee is the same for each member. Andy is 20 cents short for the fee and Larry is 8 cents short for his fee. When they combine their money, they still do not have enough money to pay the fee for even one of them. What is the maximum amount possible for the membership fee in cents? 9. Jackson and other four students A, B, C, and D are competing in a tennis tournament. Each was scheduled to play a game with each of the others. Currently, Jackson has played 4 games, student A has played 3 games. Student C has played 2 games. At least, how many game(s) has student B played? 10. Julia goes to library every 6 days. Eric goes to the library every 8 days. Richard goes to the library every 10 days. They met together in the library today. At least how many days later will they be able to meet again in the library if they all stick to their schedules? (Assume that the library is open every day). |