Choose 5 integers from the list {1, 2, 3, 4, 5, 6, 7, 8}. Show that two of the o

Question

Choose 5 integers from the list {1, 2, 3, 4, 5, 6, 7, 8}. Show that two of the ones you picked add up to 9. (2) Let S be the set {1, 2, ..., 10}. How many subsets of S of size exactly three must one have in order to know that at least two of our subsets have the same weight (=sum of the numbers in the subset)? (3) Given is a square with side length one. Someone picks 5 points in (or on the boundary of) the square. Why are there two chosen points that are squareroot 2/2 or less apart? (4) Someone is throwing a party with n people in attendance (n greaterthanorequalto 2, including the host). Why are there at least two people at the party that have exactly the same number of acquaintances present?

Explanation / Answer

Given list is {1,2,3,4,5,6,7,8}

Choose any 5 integers from the above list.

{1,2,5,7,8}

Need to show that two of the integers from {1,2,5,7,8} add up to 9.

Let's take 1,8 from {1,2,5,7,8}

1+8 = 9

Let's take 2,7 from {1,2,5,7,8}

2+7 = 9

Therefore, the two numbers from {1,2,5,7,8} add up to 9.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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