Difference between revisions of "2019 AMC 8 Problems/Problem 13"
(→Solution 1) |
(Fixed italics) |
||
| Line 1: | Line 1: | ||
==Problem 13== | ==Problem 13== | ||
| − | A | + | A ''palindrome'' is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let <math>N</math> be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of <math>N</math>? |
<math>\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6</math> | <math>\textbf{(A) }2\qquad\textbf{(B) }3\qquad\textbf{(C) }4\qquad\textbf{(D) }5\qquad\textbf{(E) }6</math> | ||
Revision as of 13:02, 21 November 2019
Contents
Problem 13
A palindrome is a number that has the same value when read from left to right or from right to left. (For example 12321 is a palindrome.) Let 
be the least three-digit integer which is not a palindrome but which is the sum of three distinct two-digit palindromes. What is the sum of the digits of ?
Solution 1
All the two digit palindromes are multiples of 11. The least 3 digit integer that is the sum of 2 two digit integers is a multiple of 11. The least 3 digit multiple of 11 is 110. The sum of the digits of 110 is 1 + 1 + 0 = 
.
~heeeeeeheeeee
Solution 2
We let the two digit palindromes be 
, 
, and 
, which sum to 
. Now, we can let 
. This means we are looking for the smallest 
such that 
and 
is not a palindrome. Thus, we test 
for , which works so 
, meaning that the sum requested is 
.
~smartninja2000
See Also
| 2019 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
