Prove that there must be two distinct integers in A whose sum is 104.

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.

Combinations Proof : 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.

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.

Fibonacci Sequence Proofs, Pascal's Triangle and Binomial Coefficients

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 expressions, and then verify the formula. a. f0 + f2 + f4 + …+f2n b. f0 - f1 + f2 - f3 + …+(-1)n fn --------------------------------------------- Practice problem 3 ...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

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

Recursively Defined Sequence : Find the 2001st Term

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

Probability : Selection Without Replacement, Combinations and a Probability Tree

Three letters from A, B, C, D, and E are selected one at a time (without replacement). a. What is the probability that they are selected in alphabetical order? b. What is the probability that they are selected in alphabetical order, if B is the first letter selected.

Probability : Selection Without Replacement

John randomly picks (without replacing) four marbles from a jar that contains 6 red and 4 blue marbles. Mary randomly picks three marbles from a jar that contains 3 red and 5 blue marbles. What is the probability that John picks more blue marbles than Mary?

A = {1,2,3} and B = {a,b,c}, and let f: A B

A = {1,2,3} and B = {a,b,c}, and let f: A -> B (a) Give an example of a one to one function from A to B. Briefly explain why your example is a 1-1 function. (b) How many one to one functions from A to B are there? Explain. (c) Define a function f^-1, for some function f from A to B. (d) Is the function g: ...continues