Let the ordering of the integers from lowest to highest be a, b, c, d and e
And we know that [a + b + c + d + e ] / 5 = 6
a + b + c + d + e = 30
And the median is 6, so....c = 6
And ... e - a = 6 → e = 6 + a
So....
a + b + c + d + e = 30
a + b + 6 + d +( 6 + a) = 30
2a + b + d = 18
b + d = 18 - 2a
[ b + d ] / 2 = 9 - a
"a" must be odd.....so...."e" must be odd
And b, d must be of the same parity....both even or both odd
And since the mode is 6, either b or d (or both ) are 6
Let a = 1 and b = 6... then d would have to be 10
But e = 7....which means that d > e......not possible
And if d = 6, then b = 10....but b > c ....not possible
So a cannot be 1
Next....let a = 3
[ b + d ] / 2 = 9 - 3
b + d = 12
So....if either b, d = 6....then the other must also = 6
So....
3 + 6 + 6 + 6 + 9 = 30 is true
The mean, mode, range and median = 6
So....the numbers are just as EP found !!!!