In my opinion the best way to solve this problem is to use 2 odds and 3 evens
For example for
Median is greater than mode and mean is greater median
10 10 11 10 29 because it would be
10=mode 11 = median and 14=mean
For mode < mean< median
For example
11675
It would be
Mode=1 mean=4 median 5
How make this work is if i want the mode to be low i put two low numbers in and to make it high i put to high numbers in.
For mean i put 3 high numbers then a medium then a low one to keep it not too small but not too big.
For the median if you wanted it to be the lowest you'd need 3 really close numbers that are low and 2 really high numbers and for highest numbers you must have 2 low numbers and three high numbers.
And for median< mode<mean
8,6,6,7,12
mode =6 median=7 mean =7.8