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, (6**7** 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**