Given that there are $20$ positive numbers and that the median is $42$, mean is $46$ and the range is $35$. An important condition, I missed: A number can appear at the most two times.
This was indeed question asked in my sister's class (6th grade). She solved it by setting
$x_1, x_2, x_9 \dots 42, 42, y_1, y_2 \dots y_9$ and found three solutions and got her assignment correct.
The values she got was
$30, 30, 31, 31, 32, 32, 33, 33, 34, 42, 42, 43, 61, 62, 63, 63, 64, 64, 65, 65$
$30, 30, 31, 31, 32, 32, 33, 33, 34, 42, 42, 55, 55, 56, 63, 63, 64, 64, 65, 65$
$30, 30, 31, 31, 32, 32, 33, 33, 34, 42, 42, 51, 54, 62, 63, 63, 64, 64, 65, 65$
I looked at this question and seemed interesting to ask what are all possible solutions?
I am therefore seeking an approach to find all possible solutions.
I attempted by listing a possibility (there could be more)
$x, x, x_1, x_2, x_3, x_4, x_5, x_6, x_7, 42, 42, y_7, y_6, y_5, y_4, y_3, y_2, x_1, x+3, x+35$
where $x_i < 42, $ and $y_i > 42$ and $7 < x < 42$
By doing a little more work, I could come with the smallest value of $x=29$. Is that correct?