Suppose you obtain a mystery bag of marbles. What you do know about this mystery

Question

Suppose you obtain a mystery bag of marbles. What you do know about this mystery bag is that each marble within is one of exactly 5 different colours: green, black, yellow, red and blue. You also know that the bag contains 504 marbles. What you do not know is how many marbles of each colour is within. For this question, you will prove, without looking in the mystery bag, that the following statement is true:

Theorem 2. The mystery bag contains at least 101 marbles of one of the five colours.

1.Give a proof by contradiction of Theorem 2. For the first step, write the negation of Theorem 2 in the box below:

2.Now, assume the negation of Theorem 2 is true, and show that this assumption leads to a contradiction.

Explanation / Answer

Let us assume that the minimum number of marbles of each color be 100. This is not possible since total number = 500 which is not equal to 504

Let green,black,yellow and red marbles be 1 each . Then blue marbles = 500

Hnece, minimum number of marbles of one of the colors is 101

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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