Calculating the nth Term of a Cartesian Product

I recently had to calculate the nth term for a Cartesian Product. I wanted to avoid generating the entire Cartesian Product in order to jump to the nth term. I wanted a way to derive the nth term.

For example, let's say I have two arrays:

a = [
  [1,2,3],
  [4,5]
]


The Cartesian Product of the above two arrays can be:

[[1, 4], [1, 5], [2, 4], [2, 5], [3, 4], [3, 5]]


Now, when I ask for the 3rd term of the above cartesian product, I want to receive [3,4]. Again, I want to do this without calculating the entire set.

My solution is below:

def combo(arrays, num)
  arrays.map do |a|
    v = a[num % a.length]
    num /= a.length
    v
  end
end


Example:

term = combo(a, 2)
puts term.inspect
# [2,4]


The next trick is to turn [2,4] back into 2.

Suggestions for how to improve this?

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