Oct 08, 2026 by Offer

Millennium HackerRank 2027: Triplets Question & Approach

The Millennium hackerrank triplets even insight: a three-number sum is even when the count of odds is even — so valid triplets are (even, even, even) or (even, odd, odd). Count evens E and odds O: answer = C(E,3) + C(O,2)xE. Commonly reported by candidates.

What This Question Assesses

This tests whether you reduce a problem before coding it. The brute-force O(n³) triple loop works on tiny inputs but signals weak problem-solving; the parity insight shows mathematical thinking. Interviewers and automated tests alike reward the combinatorial approach: it is faster, cleaner, and demonstrates the instinct to find structure before writing loops.

Millennium Hackerrank Triplets Even: How to Answer

Step 1 — State the parity rule. "odd + odd = even, even + even = even, odd + even = odd. For three numbers to sum even, the number of odds must be even: 0 or 2."
Step 2 — Enumerate the valid patterns. "All three even, or one even and two odds. (Three odds sums odd; two evens and one odd sums odd.)"
Step 3 — Count combinatorially. "With E evens and O odds: C(E,3) all-even triplets plus C(O,2)×C(E,1) mixed triplets."
Step 4 — Write clean code. One pass to count parity, then the formula. Mention the closed form C(n,k) = n(n−1)(n−2)/6.

```python def count_even_triplets(nums): evens = sum(1 for x in nums if x % 2 == 0) odds = len(nums) - evens def c3(n): return n (n - 1) (n - 2) // 6 if n >= 3 else 0 def c2(n): return n * (n - 1) // 2 if n >= 2 else 0 return c3(evens) + c2(odds) * evens ```

An example line: "Instead of checking every triplet, I use parity: an even sum needs zero or two odds, so I count evens and odds once and combine them combinatorially — linear time, constant space."

Millennium Hackerrank Triplets Even: Common Mistakes

Writing the O(n³) triple loop first. On a timed assessment it may pass small tests and time out on large ones. Lead with the parity insight.
Missing a pattern. Forgetting the (even, odd, odd) case or double-counting is the classic error — verify the parity logic on a tiny example before coding.
Integer division bugs. In languages with integer division, compute the combination carefully to avoid truncation. Test with small known values.

HackerRank-style questions reward the candidate who thinks for thirty seconds before typing — the parity observation is the whole question.

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FAQ

Why does the parity rule work? Parity adds modulo 2: odd ≡ 1, even ≡ 0. Three numbers sum to an even total exactly when an even number of them are odd — 0 or 2 out of 3.

What is the time complexity of the optimal solution? O(n) to count parities plus O(1) for the formula — versus O(n³) for brute force. Space is O(1) either way.

How do I avoid overflow in other languages? Compute combinations with division interleaved, or use 64-bit integers. For very large n, the counts themselves can exceed 32-bit range.

What follow-ups might appear? Generalisations: k-tuples summing to even, sums divisible by m (use remainder counts), or counting pairs/triplets with a target sum — all reward the same count-first instinct.

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