How to prove that a combination of 5 parameters is unique Hi everyone and thanks for reading this!
My problem:
Let's say we have a list of 100 people, each having these 5 characteristics: weight, height, age, IQ and shoe size. We know the numerical values for those. How do I prove that the combination of these parameters is / is not unique for each individual? 
I need this for a project, any input or direction anyone can give me would help tremendously, as for now I'm totally lost. 
I hope I could made myself understood, English is not my native language.
 A: To really prove they are distinct, you loop over pairs of individuals and check that each pair differs in at least one characteristic.  You can prove they are not distinct by exhibiting a pair of individuals that match or by showing there are not enough possible values.  If each of the five characteristics could only take two values, there would be only $2^5=32 \lt 100$ possible combinations, so there must be some matches.  If there are a number of possibilities for each characteristic you could argue that a match is rather unlikely.  If there were $100$ values for each characteristic, there are $100^5=10^{10}$ combinations so it is unlikely there is an exact match.  You might have a pair of twins, though, so a match is not impossible.
A: To do this algorithmically, group by height, remove groups containing only single individual. For each remaining groups, group by height, again remove groups with lone individual. Repeat for the remaining characteristics. If along the way all groups are eliminated, then you have proven that everyone is unique (although some may have many common parameters). Otherwise, you end up with groups sharing some combinations of parameters.
