Summing 4-Digit Numbers with 1,2,3,4

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In summary, the conversation discusses finding the sum of all 4-digit numbers formed by digits 1, 2, 3, and 4 with repetition. After some discussion and suggestions, the method of arranging the numbers in increasing and decreasing order is suggested, leading to the answer of twice the sum actually needed and dividing it by 2.
  • #1
The legend
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Find sum!

Homework Statement



Find sum of all 4-digit numbers formed by digits 1,2,3,4 with repetition.


The Attempt at a Solution


i did come figure out that there are 44 = 256 numbers possible but how do i sum them up without listing each individually?
 
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  • #2


Can you arrange them in increasing order? Which one is the smallest, the next and so on?
 
  • #3


ok, that would give me something like this

1111
1112
1113
1114
1121
1122
.... and so on but how will that help? :confused:
 
  • #4


why don't you look at the vertical pattern of the numbers you're writing out...
 
  • #5


ow foolish me!
so i get it there's repetition of 1+2+3+4 in units and in tens 1+1+1+1+2+2+2+2... so on and adding them a bit cleverly(though it does consume some time!) as you guys suggested and I got the answer.
so thanks for helping me out! :approve:
 
  • #6


I would make an other column beside this one, but the numbers would be in decreasing order...

ehild
 
  • #7


oh .. i see.. this is even quite easier than i suspected!

Thanks again! :smile:
 
  • #8


... so what did you come up with?
 
  • #9


ehild said:
I would make an other column beside this one, but the numbers would be in decreasing order...

ehild

and I would add up the two numbers in one row...

ehild
 
  • #10


adding up as ehild said i get same terms ie= 5555 256 times!
so what would happen is we get twice the sum actually needed and dividing it by 2 ... easy answer!
 

FAQ: Summing 4-Digit Numbers with 1,2,3,4

How do you sum 4-digit numbers with 1,2,3,4?

To sum 4-digit numbers with 1,2,3,4, you simply add each digit in the same place value together. For example, if you have the numbers 1234 and 4321, you would add 1+4, 2+3, 3+2, and 4+1 to get the sum of 5555.

Can you provide an example of summing 4-digit numbers with 1,2,3,4?

Of course. Let's say we have the numbers 1432 and 3214. We would add 1+3, 4+2, 3+1, and 2+4 to get the sum of 4646.

3. Is there a specific order in which the numbers should be added?

No, there is no specific order in which the numbers should be added. You can add them in any order and the result will be the same.

4. Can you sum more than two 4-digit numbers with 1,2,3,4?

Yes, you can sum more than two 4-digit numbers with 1,2,3,4. The method is the same - add each digit in the same place value together. For example, if you have the numbers 1234, 4321, and 2468, you would add 1+4+2, 2+3+4, 3+2+6, and 4+1+8 to get the sum of 8634.

5. Can you use this method for summing numbers with more or less than 4 digits?

Yes, this method can be used for summing numbers with any number of digits. You simply add each digit in the same place value together. For example, if you have the numbers 12, 345, and 6789, you would add 1+3+6, 2+4+7, and 5+8+9 to get the sum of 33, 47, and 22, which would then be added together to get the final sum of 102.

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