Difference between revisions of "2009 AMC 10B Problems/Problem 11"
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== Solution == | == Solution == | ||
| − | A seven-digit palindrome is a number of the form <math>\overline{abcdcba}</math>. Clearly, <math>d</math> must be <math>5</math>, as we have an odd number of fives. We are then left with <math>\{a,b,c\} = \{2,3,5\}</math>. Each of the <math>\boxed{6}</math> permutations of the set <math>\{2,3,5\}</math> will give us one palindrome. | + | A seven-digit palindrome is a number of the form <math>\overline{abcdcba}</math>. Clearly, <math>d</math> must be <math>5</math>, as we have an odd number of fives. We are then left with <math>\{a,b,c\} = \{2,3,5\}</math>. Each of the <math>\boxed{(A)6}</math> permutations of the set <math>\{2,3,5\}</math> will give us one palindrome. |
== See Also == | == See Also == | ||
Revision as of 00:49, 16 January 2020
Problem
How many 
-digit palindromes (numbers that read the same backward as forward) can be formed using the digits 
, , 
, , 
, , ?
Solution
A seven-digit palindrome is a number of the form 
. Clearly, 
must be , as we have an odd number of fives. We are then left with 
. Each of the 
permutations of the set 
will give us one palindrome.
See Also
| 2009 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AMC 10 Problems and Solutions | ||
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