Back to our discussion, I bet you couldn't come up with a number for the following: the number of sets of thirteen numbers in the range of 16 to 175.
Each number can appear more than once, and the order matters as well. Eliminate all the sets totalling less than a 1000, and more than 1452 (a realistic range for engraving sizes). I'm sure you can put it into numbers, but not words, since you probably don't know the name of that particular astronomical number.
First where do you get the satement "a realistic range for engraving sizes"? What science, study, or example to you have to support this or is this just something you pulled from your assumptions (and what exactly is the range 1000 to 1452 pixels?, inches? and is this a side length or the area? How does it define the picture?)
The number of sets by the way, is clearly infinite
Set 1. 77 repeated 13 times
Set 2 77 repeated 12 times followed by 77.1
Set 3 77 Repeated 12 times followed by 77.11
Set 4 77 Repeated 12 times followed by 77.111
Well I demonstrate it obviously with my example, but I think I can do a real proof here:
Any Set of 13 numbers containing {77,77,77,77,77,77,77,77,77,77,77,77,77} Has a sum greater than 1000 but less than 1452. ====> 77 * 12+ 77 = 1001
Any Set of 13 numbers containing {77,77,77,77,77,77,77,77,77,77,77,77,78} in any order has a sum greater than 1000 but less than 1452======> 77*12+78=1002
Their are infinate numbers X, where 77<=x<=78
Therefore there are infinite lists containting {77,77,77,77,77,77,77,77,77,77,77,77,X} where 1001<=77*12+X<=1002
Therefore there are infinite lists of 13 numbers where the sum of the numbers greater than 1000 and less than 1425
QED
Now maybe you meant whole real numbers, but I would just say any measurment you make would likely not consist of such numbers. If all your measurments were somehow comming out to such miracoulous numbers, it would still be on you to verify this by actually using the real object instead of measuring a copy which in and of itself makes your work less acurate.