Min value of 0 occurs when x = 0
Max value of 1166 occurs when x = 100
So, the number of distinct possible values is less than or equal to 1167.
Are all of those values achievable? No, they are not.
For instance, when x = 1, the expression equals 1*10 + floor(5/3) = 11.
But, when x is slightly less than 1 it is 4 less. So, 10 and 9 and 8 are not achievable.
This occurs whenever x is an integer not divisible by 3, so it is the case for x = 1,2,4,5,7,8...97,98, 100.
All together, (67 values of x) * 3 = 201 impossible values
The situation is slightly different when x is divisible by 3.
For instance, when x = 3, the expression equals 3*10 + floor(5*3/3) = 35.
But, when x is slightly less than 3 it is 5 less. So, 34 and 33 and 32 and 31 are not achievable.
All together, (33 values of x) * 4 = 132 impossible values.
Also, 2 and 4 are not relatively prime, so we lose some values when x is a multiple of 1/2 but not 1.
For instance, when x = 1/2, expression = 0 + 1 + 0 + 1 + 2 = 4
But, when x is slightly less than 1/2 it is 2 less. So, 3 is not achievable.
All together, (100 values of x) * 1 = 100 impossible values.
Total achievable values = 1167 - 201 - 132 - 100 = 734
Edited on October 20, 2015, 7:27 pm
Is the answer an airplane model? (Spoiler?)
