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I tried to find out the all numbers or set of possible combination of numbers. But I have only the averages value, maximum number, minimum number & also have tolal number of numbers.

Example:
Avg value: 150
Max number: 500
Min number: 33
Total numbers: 11

I need to find out all number or set of combination of those 11 number.
SOYON
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2 Answers2

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(1) No, it's not possible in the general case to find the numbers unambiguously. Only on some boundary cases it may be possible to find the 11 numbers unambiguously. Why is it not possible? Say you have 11 numbers satisfying your conditions. Then take two of them a and b which are neither the min, nor the max. Then pick any number c such that a+c, b-c are neither equal to the min, nor to the max. Now observe that if you substitute a with a+c, and b with b-c then you get another 11 numbers satisfying your conditions. Normally you can find many such values for c. Now, as you can vary c, you get many possible combinations of 11 numbers.

(2) You can though construct one sample set satisfying your conditions. Take e.g. these 11 numbers: the min, the max, then 9 times the number (sum-min-max)/9. These 11 numbers satisfy your conditions. Note: here sum = 11 * avg.

peter.petrov
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1

If the total number of numbers is $3$, then yes. And if the maximum and minimum values are the same, also yes. Otherwise, no.

For example, in your particular case, you know that one number is equal to $500$, one is equal to $300$, and, because their average is $150$, you know that the sum of all the numbers is $1650$. Thus, any combination of $9$ numbers from the range $[33, 500]$ that sums to $1117$ will return the average, max and min values you wrote down.

For example:

500,33,100,100,100,100,100,100,117,200,200

is one possibility, and

500,33,100,100,100,100,100,100,217,200,100

is another.

5xum
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