Partitioning List Into Sublists of Length 2 With The Pairing Being Random

Question

I've done a bit of Googling with hopes of finding an answer, but to no avail. I'm looking for a way that I can have Mathematica take the elements of a list, say {a,b,c,d}, and partition the elements into lists of length 2 but allowing the grouping of these elements to be random. The Partition function nearly produces the desired results, but groups the elements in {a,b,c,d} in the order they appear (i.e. the result is {{a,b},{c,d}}) when I would like a random pairing such as {{a,d},{c,b}}.

Is there some way of utilizing the Partition function so that it allows me achieve this? Or there perhaps another built-in function or combination of built-in functions that do this?

Thank you all so very much.

Answer 1

While David G. Stork's solution works it is not efficient. You are generating all possible tuples and then selecting them randomly. Try this with a list of 19 elements in tuples of 10 and you will be waiting forever.

This solution should work just fine with lists of any length

list = {a, b, c, d};
Partition[
    RandomSample[list]
 , 2]

{{c, d}, {b, a}}

@Qwerty to produce a specific number of pairs, you should try something like this:

list = {a, b, c, d, e, f, g};
numberOfPairs = 3;
Partition[
    RandomSample[list, numberOfPairs*2]
 , 2]

{{f, a}, {g, c}, {e, d}} 

Note that Length@list must be greater or equal to 2*numberOfPairs

Answer 2

RandomSample[Tuples[{a, b, c, d}, 2]]

If you want a fixed number of pairs (say 5):

Take[RandomSample[Tuples[{a, b, c, d}, 2]], 5]

Answer 3

Could this work for your problem?

A = {a, b, c, d, e, f, g}
list = Union[Flatten[Map[Partition[#, 2] &, Permutations[A]], 1]]
Extract[list, RandomInteger[{1, Length[list]}]]

Change the predicate in the Partition function for different lengths.

f[_] := Extract[list, RandomInteger[{1, Length[list]}]]
Array[f, 10]

will generate 10 subsets for (pseudo)random pairs.