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 == |
Latest 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 | |
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All AMC 10 Problems and Solutions |
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