- #1
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What is the sum of all the numbers formed by taking each of the digits 2,3,5,6 and 8 once?
Numbers formed by taking each of the digits 2,3,5,6 and 8 once?
- Context: High School
- Thread starter Greg Bernhardt
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Discussion Overview
The discussion revolves around calculating the sum of all possible 5-digit numbers formed by using the digits 2, 3, 5, 6, and 8 exactly once. It explores combinatorial reasoning and different approaches to arrive at the total sum.
Discussion Character
- Mathematical reasoning
- Exploratory
- Debate/contested
Main Points Raised
- One participant initially claims the sum of all numbers formed is 6399936, but does not provide a clear method for this calculation.
- Another participant calculates the number of permutations of the digits, stating there are 120 permutations and that the sum of the digits is 24, leading to a total of 2880 for the sum of all permutations.
- A later reply suggests that each digit appears 24 times in each column for the 5-digit numbers, leading to the same sum of 6399936 through a different calculation method, but later clarifies a misunderstanding regarding the question's intent.
- One participant proposes an alternative calculation method using factorials and the sum of the digits, arriving at the same total of 6399936.
Areas of Agreement / Disagreement
There is no consensus on the correct total sum, as participants present differing calculations and interpretations of the question. Some methods yield 2880 while others yield 6399936, indicating competing views remain.
Contextual Notes
The discussion includes various assumptions about the interpretation of the question, particularly regarding whether it pertains to the sum of the numbers formed or the sum of their digits. The calculations also depend on the understanding of permutations and the distribution of digits across different positions.
- #2
BoulderHead
haha, maybe later.
- #3
jamesrc
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6399936
- #4
- 19,917
- 10,945
How'd you get that answer?
- #5
redrogue
- 32
- 1
Hmm...combinatorics.
2 3 5 6 8
There are: (5)*(5-1)*(5-2)*(5-3)*(5-4) or 5*4*3*2*1 = 120 permutations for the above set of numbers.
One set of numbers add up to: 2+3+5+6+8 = 24.
So, the sum of all numbers formed from 120 permutations is:
120*24 = 2880.
2 3 5 6 8
There are: (5)*(5-1)*(5-2)*(5-3)*(5-4) or 5*4*3*2*1 = 120 permutations for the above set of numbers.
One set of numbers add up to: 2+3+5+6+8 = 24.
So, the sum of all numbers formed from 120 permutations is:
120*24 = 2880.
- #6
jamesrc
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If I answered the right question, for all of the 5-digit numbers you can make, each digit appears 24 times in each column, so you can write:
24*(22222+33333+55555+66666+88888)=6399936
Edit: Oh, I thought it was the sum of the numbers made by the combinations, not the sum of their digits.
24*(22222+33333+55555+66666+88888)=6399936
Edit: Oh, I thought it was the sum of the numbers made by the combinations, not the sum of their digits.
Last edited:
- #7
- 19,917
- 10,945
James gets the point!
Here is an alternative way:
4!*(2+3+5+6+8)*(11111) = 6,399,936
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