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1,234+1,243+1324+...+4321 The addition problem above shows

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1,234+1,243+1324+...+4321 The addition problem above shows [#permalink] New post 29 Mar 2008, 03:22
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1,234+1,243+1324+...+4321
The addition problem above shows four of the 24 different integers that can be performed by using each of the digits 1, 2, 3 and 4 exactly once in each integer. What is the sum of these 24 integers?

Please advice shortcut to this problem.
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Re: PS (permutation) [#permalink] New post 29 Mar 2008, 03:43
1,234 + 1,243 + 1,324 +...+ 4,321

= Grand total of [6 x n x 1,000 + 6 x n x 100 + 6 x n x 10 + 6 x n x 1 ] with n = 1-> 4
= 6 x 1,000 x (1+2+3+4)
+ 6 x 100 x (1+2+3+4)
+ 6 x 10 x (1+2+3+4)
+ 6 x 1 x (1+2+3+4)
= 66,660

So the answer is 66,660.
Re: PS (permutation)   [#permalink] 29 Mar 2008, 03:43
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