Discrete Mathematics

posted by .

It was proven during the previous lecture that
1+2+3+....+n=[n(n+1)]/2.

Using that result, find the sum of all 3-digit palindromes: a palindrome is a number that can be written as ABA, where 1=<A<=9 and 0<=B<=9. Hint: decompose ABA = 100*A + 10*B + A and use above proven result.

  • Discrete Mathematics -

    Note that A can vary from 1 to 9, while B can take on the digits 0 to 9.

    Sum of first and third digits:
    So for each value of A=a(i), the sum is 100a(i)+a(i)=101a(i).
    For the 9 values of A, we have a sum of
    101Σi for i=1 to 9.

    Since each value of a(i) can be matched to 10 values of B, the above sum has to be multiplied by 10 to give
    1010Σi for i=1 to 9.

    Sum of the second digit (B)
    Each digit of B is in the 10 position, so we need to multiply by 10.
    The sum of the digits 0-9 are repeated 9 times for each value of A, so the sum of digits B is
    9*10Σi for i=0 to 9
    =90Σi for i=0 to 9

    Finally, add up the two sums:

    1010Σi for i=1 to 9.
    +
    90Σi for i=0 to 9

    to get the total

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Palindromes

    What is a palindrome that means excitement. What is a palindrome for Old cats who are forgetful (2 words) What is a palindrome for a hippie with no name (what would he say?
  2. PALINDROMES

    ON THE NUMERS 10 AND 100, HOW MANY OF THEM ARE PALINDROMES?
  3. Math

    How many bit strings of length n are palindromes?
  4. math

    Solve if each letter is a different digit. ABA + CBC CBCB -
  5. Math

    It is a 5 digit no. ,palindrome,divisible by 4,10 digit is cube root of 1 digit,product of 100 digit and 1 digit is 54 ,sum of hundred and ones digit is 15.what is the number?
  6. Algebra math.

    1) the sum of the digits of a two digit number is 9. The value of the number is 12 times the tens digit. Find the number. 2) the sum of the digits of a two digit number is 12. If 15 is added to the number the result is 6times the units …
  7. algebra

    A palindrome is a number that reads the same forwards as it does backwards. For example, 98789 is a 5-digit palindrome, and 7337 is a 4-digit palindrome. How many 3-digit palindromes are there?
  8. maths

    Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has …
  9. Algebra - Math HW HELP!

    1) It is a five-digit whole number. 2) It is a palindrome. 3) Its tens digit is the cube root of a one-digit number. 4) The product of its hundreds digit and its ones digit is 54. 5) The sum of its hundreds digit and its ones digit …
  10. math

    Numbers that are palindromes read the same forward and backward. For example, 30203 is a five digit palindrome. If a single number is chosen randomly from the set of all three-digit numbers, find the probability that it will be palindromic. …

More Similar Questions