Least and Most( Week 16 Evaluation) 1. There are 60 balls of 6 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 4 balls which are the same color? 2. If humans have up to 110,000 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 115,000 people? 5. A bag contains 400 beads. All the beads are the same, but in 5 different colors. There are equal number of beads for each color. If Helen 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 15 beads of the same color? 6. A bag contains 581 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 Josh picks the beads blindfolded, at least how many beads will Josh 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 98, at least how many numbers need to be picked to make sure that there is at least one number which is a multiple of 4? 8. Kevin and David want to pay their membership fee in a MODEL club. The membership fee is the same for each member. Kevin is 21 cents short for the fee and David is 6 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. Steve 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, Steve has played 4 games, student A has played 3 games. Student C has played 2 games. At least, how many game(s) has student D played? 10. Morgan goes to library every 6 days. Ed goes to the library every 8 days. Ben 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). |