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A number is called swappy if it is not a palindrome, but swapping two of its digits produces a six-digit palindrome. For example, the number 813381 is swappy, because we can swap the last two digits to get 813318, which is a palindrome.

How many swappy six-digit numbers are there?

 Feb 16, 2020
 #1
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There are C(4,2)*C(4,2)*(10 - 1) = 6*6*9 = 324 swappy numbers.

 Feb 16, 2020
 #2
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See answers #1 and #2 here:  https://web2.0calc.com/questions/counting-probability

 Feb 16, 2020

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