Pigeon hole principle

Pigeon hole principle

Twenty distinct integers are arranged in a list in a random order, such that all 20! orderings are equally likely. Going down the list, one marks every number that is larger than all earlier numbers...

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that xn+6=xn for all n belonging to N using the below formula xn=p((1+i(sqrt3))/2)n+q((1-i(sqrt3))/2)n p...

security codes are made of 3 letters followed by four single digit numbers. How many different 7 character security codes can be made if none of the letters can repeat and the first digit must be...

use the well-ordering principle. Please help with this question, it's a practice problem, I just can't figure out. Thank you!

let m,n belong to N, and m,n>1, prove that mn< (m+n)choose 2 Please help. Thank you!

Given the information x1=1 and x2=2, and ∀ n≥2, xn+1=4xn-5xn-1, find explicitly the values of p,q which make xn=p(2+i)n+q(2+i)n for every n. I am really having...

suppose that in solving a tsp you use the cheapest link algorithm and find a cheapest link tour with a length of 21400 miles. suppose that you later find out that the length of an optimal tour is...

For a 2 coin toss experiment, what are the set of events that are statistically independent when you assume: a) equally likely outcomes b) not equally likely outcomes

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that ∀ n ∈ N, xn+6=xn by induction Please help me. I'm reviewing for my final and something...

let 〈xn〉n=1...∞ be a sequence satisfying xn+1=xn-xn-1 for each n. Prove that ∀ n ∈ N, xn+6=xn by induction

let G=(V,E) be a graph where V={A⊆N5||A|=2} and E={{A,B}⊆V|A∩B=ø} sketch this graph and find its size

let n∈N. if a,b,c,d ∈ N and a≡b (mod n) and c≡d (mod n) prove that ac≡bd (mod n). Please, any help would be greatly appreciated. This is a study question on my study guide and I'm having...

Please help! I do not know how to do this practice problem. My professor told us to try it for fun. But, he never went over it in class. And now im curious

A club has 30 members under the age of 30 and 40 members who are 30 or older. In how many ways can a slate of officers be chosen if the President and atleast one other officer must be at least 30...

please help, Im very confused. This one on my exam and I didnt understand it at all. Want to know the answer so I can study for my final.

prove that for every n∈N , ( 2n choose n) is even

prove that there does not exist n∈N such that n≡2 (mod 4) and n≡4 (mod 8). Please help this was on my last exam but I was very lost and my professor did not have enough time to go over it in class...

Please help! its a combinations question. Thank you!

Numbers come in many different styles, patterns and sizes. Some numbers are big, some are small. Some numbers can be written in many different formats as well. Specific focus will be given to numbers...

Wesley P.

Ivy League 4.0 GPA Math Major, Financier

New York, NY

Evan R.

Former math instructor happy to help

New York, NY

Andrew H.

Light Bulb Lessons to Encourage Brilliant Minds

Scarsdale, NY

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