five digit integer 3.4.5.6.7

Nekkamath

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Nov 19, 2007
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Consider all of the positive five digit integers that can be formed using each of the digits 3,4,5,6,7 exactly once. What is the sum of these integers?

7 x 6 x 4
70 x 24
700 x 24
7000 x 24
70000x 24

I did this for each number (3,4,5,6) to come up with a grand total of 6,666,6000
 

soroban

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Jan 28, 2005
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5,588
Hello, Nekkamath!

Sorry, I don't understand your solution . . . but your answer is correct!


Consider all of the positive five digit integers that can be formed
using each of the digits 3,4,5,6,7 exactly once.
What is the sum of these integers?

I approached it like this . . .

\(\displaystyle \text{Consider the list of }5! = 120\text{ permuations of those digits.}\)

. . \(\displaystyle \begin{array}{c}34567 \\ 34576 \\ 34657 \\ 34675 \\ 34756 \\ 34765 \\ \vdots \\ 76453 \\ 76534 \\76543 \end{array}\)


\(\displaystyle \text{In each column, each digit appears 24 times.}\)
. . \(\displaystyle \text{Hence, each column has a total of: }24 \times (3+4+5+6+7) \;=\;600\)


\(\displaystyle \text{The addition looks like this:}\)

. . . . . . . . . \(\displaystyle 6\:0\:0\)
. . . . . . . .\(\displaystyle 6\:0\:0\)
. . . . . . \(\displaystyle 6\:0\:0\)
. . . . .\(\displaystyle 6\:0\:0\)
. . . \(\displaystyle 6\:0\:0\)
. . .\(\displaystyle - - - - - -\)
. . . \(\displaystyle 6\:6\:6\:6\:6\:0\:0\)

 

Nekkamath

New member
Joined
Nov 19, 2007
Messages
42
Thanks for your help.
 
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