Open Middle®
Directions: Create a set of five positive integers from 1 to 20 so that the values of their mean, median, and range are the same and have the greatest possible value.
Hint
How do you find the mean/median/range of a set of five integers?
Answer
The greatest possible value found so far is 14 from the data set {6, 11, 14, 19, 20}.
Source: Eric Berchtold, Melissa Minnix, and Robert Kaplinsky
This is a neat puzzle.
I think that 5, 15, 15, 20, 20 would work.
Range: 15
Median: 15
Mean: 75/5 = 15
You can’t use numbers twice
The problem doesn’t state that there are no repeats.
2,3,4,5,6
Mean=4
Median=4
Range=4
[6, 13, 14, 17, 20] and [6, 12, 14, 18, 20] and [6, 11, 14, 19, 20] are the (only) solutions with the greatest possible mean=median=range, if you don’t allow repeated numbers
[5, 15, 15, 20, 20] is the (only) solution if you allow repeated numbers.
4, 9, 10, 13, and 14 works as well, not the greatest, but a solution nonetheless.