Discrete mathematics

I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. 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.

100 = 1 + 3(n-1) = 3n -2,
n = 34
Totally, there are 34 terms from
Among them there are 16 pairs can from 104 are:
4, 100
7, 97
10, 94
46, 58
49, 55 (=3*16+1, 103-3*16)
as (boy girl)

If no two chosen numbers whose sum
is 104, then we only can choose one
from the above pairs.
That is, we can at most choose
16+1+1 = 18 numbers among 34 where
no two whose sum is 104.
However, we choose 20 > 18 numbers
so at least two with sum 104.

This answer may be late, since I saw
this question a short while ago.


  1. 👍 0
  2. 👎 0
  3. 👁 295

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    Could someone check my work; 1. Generate the first five terms in the sequence using the explicit formula. yn = –5n – 5 –30, –25, –20, –15, –10 30, 25, 20, 15, 10 –10, –15, –20, –25, –30(my answer) 10, 15,

    asked by lee on February 3, 2013
  2. Math (pre-calculus)

    Hi! I have a question! I forgot how to do these two problems, and I need some help in solving them! Thanks so much! 1.) Find the first 5 terms of the sequence given by a1=2, an=3an-1 -1. (It's: a sub 1 =2, a sub n= 3a sub n-1 -1)

    asked by Angellove on November 2, 2008
  3. algebra

    Explain the difference between solving a system of equations by the algebraic method and the graphical method. Someone also wants to know why there are different methods for solving the same problem-what would you tell him?

    asked by kiMBERLY on July 12, 2010
  4. Physics

    A snowmobile, with a mass of 530 kg, applied a force of 410 N backwards on the snow. a) What force is responsible for the snowmobile’s resulting forward motion? (Hint: Think action–reaction force pairs.) b) If the force of

    asked by Dan on March 28, 2014
  1. Physics

    A 1200 kg car pulls an 820 kg trailer over a rough road. The force of friction acting on the trailer is 650 N [backwards]. Calculate the force that the car exerts on the trailer if (a) the trailer is moving at a constant velocity

    asked by Jenuson on November 16, 2014
  2. English

    From time to time, companies will issue a reverse split concurrently with a forward split, making a reverse/forward split. Note that in reverse/forward splits, the shareholder's old shares are erased, as they receive a number of

    asked by rfvv on July 7, 2020
  3. Pre-Calc

    Find three examples of the Fibonacci sequence in nature. Write a paragraph for each example. For each example, address the following questions: How does the example relate to the Fibonacci sequence? What portions of each item or

    asked by Anonymous on September 11, 2011
  4. newton's method #2

    i want to verify that when newton's method is used to compute sqrt(R) (by solving the equation x^2=R), the sequence o iterates is defined by x_(n+1)=.5(x_(n) + (R/x_(n))

    asked by Julie on September 28, 2008
  1. physics

    A quarterback takes the ball from the line of scrimmage, runs backwards for 9.0 yards, then runs sideways parallel to the line of scrimmage for 17.0 yards. At this point, he throws a 46.0-yard forward pass straight downfield,

    asked by Anonymous on September 27, 2015
  2. ASL

    How is the sign WEEK modified to indicate last week? (3 points) A backwards movement is added. ************** A forward movement is added. L-A-S-T is added. There is no difference. 2. How is the sign MONTH modified to indicate

    asked by yeet my horse to the old town road on May 29, 2019
  3. Math sequence

    Let {An} be the sequence defined recursively by A1=sqr(2) and A(n+1) = sqr(2+An) for n is bigger and equal to 1. Show that An < 2. What is An? and how do I find it? Thank you for your time. An is the nth number in the sequence,

    asked by Belle on January 7, 2007
  4. math

    Two horizontal forces act on a wagon, 550N forward and 300N backwards. What force is need to produce a net force of zero? 500 N 300N -----> Object

    asked by johanna on February 5, 2016

You can view more similar questions or ask a new question.