2)How many arrangements of the integers 1,2,3,...,n are there such that each integer differs by one (except for the first integer) from some integer to the left of it?

Let's construct the arrangement.
First consider 1, it can only have two placed next to it so it has to be at the end or beginning. Do you see why?
Ok, so let's suppose the arrangement starts with 1, then the only number that can come after it is 2, then 3 then 4...
Now suppose 1 is at the end. Then the only number that can come before is 2, then 3 then 4...
The only two arrangements are
1 2 3 4 5 ... n-1 n and
n (n-1) (n-2) ... 3 2 1
By the way, we are not constructing a digit, but rather an arrangement for the first n integers.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths

    The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?

  2. math

    which of the following is a true statement? a. when comparing two integers, the integer with the greater absolute value is always the greater integer. b. when comparing two integers, the integer with the greater absolute value

  3. Math(1 question plz help thanks!=D

    if two integers have the same absolute value which of the following is true about the integers? A. they must be the same integer B. they must be the opposite integer*** C. they could be the same or opposite integer (plz help my

  4. math

    For 5 consecutive even integers, the sum of the first and third integer is 20 less than 3 times the fourth integer. What is the fifth integer?

  1. math

    An integer is 5 more than another integer. Three times the bigger integer is 11 more than the square of the smaller integer. find the two integers

  2. Math

    Tell whether the difference between the two integers is always, sometimes, or never positive. 1)Two positive integers. Never 2)Two negative integers. Sometimes. 3)A positive integer and a negative integer. Sometimes. 4)A negative

  3. quad. eq.

    find 3 consecutive integers such that the product of the second and third integer is 20 Take three integers x, y, and z. The for xyz, we want y*z = 20 The factors of 20 are 20*1 10*2 5*4. 20*1 are not consecutive. 10*2 are not

  4. Ic

    Write an application that prompts the user for two integers and then prompts the user to enter an option as follows: 1 to add the two integers, 2 to subtract the second integer from the first, 3 to multiply the integers, and 4 to

  1. Algebra

    The sum of two consecutive even integers is 118. A. Define a variable for the smaller integer. B. What must you add to an even integer to get the next greater even integer? C. Write an expression for the second integer. D. Write

  2. Math

    Explain how you can determine the sign of the sum of two integers if one integer is positive and the other integer is negative.

  3. algebra 101

    the sum of two integers is 10. three times one integer is 3 less than 8 times the other integer. find the integers. (hint: if one number is x, then the other number is 10-x.) show work please

  4. la sallle

    There are 3 consecutive even integers such that the quotient obtained by dividing twice the largest integer by the smallest integer is three less than three-fifths of the second integer. What are the integers?

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