Problem Solving

Determine the sum of the integers among the first 1000 positive integers, which are not divisible by 4 or are not divisible by 9. (This is not an exclusive.) Let R be the region consisting of points (x,y) in the Cartesian plane satisfying both the absolute value of x - the absolute value of y ≤ 1 and the absolute valu ...continues

Pigeon hole theorem (I believe)

Okay, here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression 1, 4, 7, ...,100. Prove that there must be two distinct integers in A whose sum is 104.

Formula used to determine the number of different ways to deal ...

Show that 2(2^n-1 - 1) is the formula used to determine the number of different ways to deal n distinct playing cards to two players where each player gets at least one card. I want to allow the possibility of giving a different number of cards to each player.

Problem Solving: Proofs & Sequences

Please help me with these three problems. I am a novice at writing proofs and deriving formulas so, I am not sure if I am on the right track. Questions (also attached): Practice problem 1 Fn is the Fibonacci sequence (f0 = 0, f1 = 1, fn+1 = fn + fn-1). By considering examples, determine a formula for the following e ...continues

Sum of series

Determine the sum of the integers among the first 1000 positive integers which are not divisible by 4 or are not divisible by 9. (This is not an exclusive or)

Zeno's Paradox

SUPPOSE THAT A MAN WANTS TO CROSS TO THE FAR WALL OF A ROOM THAT IS 20FT ACROSS. FIRST HE CROSSES HALF OF THE DISTANCE TO REACH THE 10 FT MARK. NEXT HE CROSSES HALFWAY ACROSS THE REMAINING 10 FT TO ARRIVE AT THE 5 FT MARK. DIVIDING THE DISTANCE IN HALF AGAIN HE CROSSES TO THE 2.5 FT MARK AND CONTINUES TO CROSS THE ROOM IN THIS W ...continues

Problem solving using discrete structures

We worked on the attached problems today in class I am now trying to work through them again for understanding and I am not getting very far. My skills in discrete mathematics are not such that I can work through these on my own effectively. 3. Seven points are located in a plane. List the possible numbers of lines determi ...continues

Sequence defined recursively

4. A sequence is define recursively by A0 = A, and An+1 = An /1 + nAn. Determine A2001.

Problem of Probability

What is the probability that three letters from a set of five, picked one at a time will be in alphabetical order? I understand probability but unable to process at this time. Please help with the attached problem.

Problem of probability

Two individuals randomly picks marbles from different jars. What is the probability the one will pick more of one color then the other. I believe I can use the combination formula to solve, but am not sure how to apply it to this quesiton.