Find the 9 Values of a Set of Positive Integers

In summary, the arithmetic mean of a set of nine different positive integers is 123456789, and each number in the set contains a different number of digits with the greatest value being a nine-digit number. To find the value of each of the nine numbers, you can use the fact that 123456789 can be expressed as 1+11+111+1111...111111111 and multiply it by 9 to get the sum of the nine numbers. Since the values must be maximal, there is only one correct answer.
  • #1
PrudensOptimus
641
0
The arithmetic mean of a set of nine different positive integers is 123456789. Each number in the set contains a different number of digits with the greatest value being a nine-digit number. Find the value of each of the nine numbers .
 
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  • #2
9,99,999,9999,99999,999999,9999999,99999999,999999999
 
  • #3
how?
 
  • #4
The only conceivable way there could be a unique answer is if all the numbers involved had some maximality/minimality conditions imposed on them (ias x+y=x-1+y+1, then any unqueness here must expliot some maximality of y or minimality of x; we have a maxmial number 999,999,999) . By inspection one sees that 123456789*9 can only be the sum of numbers satisfying your conditions if they are maximal wrt the constraints.

Also it's clear that 123456798
=1+11+111+1,111+...111,111,111, which should give another hint
 
  • #5
I immediately recognized that 123456789 = 1+11+111+1111...111111111, like Grime said. Knowing this, multiply both sides by 9, and find the answer.

Also like Grime said, the values must be that maximums, which means that there is only one correct answer.
 

What is the purpose of finding the 9 values of a set of positive integers?

The purpose of finding the 9 values of a set of positive integers is to gain a better understanding of the data and to identify any patterns or relationships within the set.

How do you find the 9 values of a set of positive integers?

To find the 9 values of a set of positive integers, you need to first arrange the numbers in ascending order. Then, you can identify the minimum and maximum values, the median, and the mode. Lastly, you can find the range, interquartile range, and mean of the set.

What is the difference between range and interquartile range?

Range is the difference between the maximum and minimum values in a set, while interquartile range is the difference between the upper and lower quartiles. Range can be affected by outliers, while interquartile range is more resistant to outliers and gives a better representation of the spread of the data.

Why is it important to find the 9 values of a set of positive integers?

Finding the 9 values of a set of positive integers allows you to summarize the data and make comparisons between different sets. It also helps in identifying any outliers or unusual values that may affect the overall interpretation of the data.

Can the 9 values of a set of positive integers change if the set is expanded?

Yes, the 9 values of a set of positive integers can change if the set is expanded. This is because the new data points will affect the mean, median, and mode, and possibly the range and interquartile range as well. However, the minimum and maximum values will remain the same unless new data points are added that are larger or smaller than the existing ones.

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