selis 4 A. A team wishes to purchase 12 shirts of the same color. A store shirts

Question

selis 4 A. A team wishes to purchase 12 shirts of the same color. A store shirts in different colors. What must the inventory of the store be in order to conclude that there at least 12 shirts in one of the four colors? B. A team of 3 high jumpers all have a personal record that is at least 6 feet and less than 7 feet. Is it necessarily true that two of the team members must have personal records that are within four inches of each other? What if there are four jumpers? C. A round-robin tournament is one where each player plays each of the other players exactly once. Prove that if no person loses all his games, then there must be two players with the same number of wins.

Explanation / Answer

Solution:

Store must have 49 shirts at least to ensure there are at least 12 of one color. We can show this by Pigeonhole principle.

Let there be 4 boxes for each color and we put a shirt in each box if it is of that color

So in worst case there can be 12 of each type in separate boxes but that would still account for only 48 shirts and the remaining 1 shirt can be put in one of the four boxes and that will make sure at least one of the boxes has 12 shirts ie there are 12 shirts of one color

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.