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How it works
Excluding the mandatory triangular padding, we're left with:
Which can minimally be explained as: Push all STDIN as an array of strings (representing each line of input), count the occurrences of all of STDIN's elements in itself (which, in case all are distinct, should yield [1, 1, 1]), sum, then check whether the sum is equal to 3. There are 2 tricks here (which together save no less than 14 bytes):
i and treating the inputs as strings rather than integers – which is quite uncommon, as
)IE is frequently used instead, taking input as a list.
- Instead of checking whether they all are equal to 1 and then taking the product – or equivalently, taking the product and checking whether it is equal to 1 – this takes the sum and compares it with 3. Proving the validity of this method is obviously trivial: [1, 1, 1] is the only valid way to partition 3 into 3 positive integers summing to it and the contents of this list are always positive, as every element of a collection must occur at least once in it :P.