Sum of All Subset XOR Totals
A easy-tier problem at 90% community acceptance, tagged with Array, Math, Backtracking. Reported in interviews at Microsoft and 0 others.
Sum of All Subset XOR Totals looks easy because it is, but it's the kind of problem that catches candidates off-guard when they haven't drilled subset generation before. Microsoft has asked it. The acceptance rate sits at 90%, which sounds safe until you realize most people who pass either knew the trick going in or brute-forced it during the OA. You're generating every subset of an array, XORing the elements in each one, then summing those totals. The naive approach works, but there's a pattern that makes it almost trivial once you see it. If you hit this live and freeze on how to enumerate subsets efficiently, StealthCoder surfaces the working solution in seconds, invisible to the proctor.
Companies that ask "Sum of All Subset XOR Totals"
Sum of All Subset XOR Totals is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE.
Get StealthCoderThe obvious move is backtracking: build every subset, compute its XOR, accumulate the sum. That's fine and it passes. But the real insight is mathematical. Each element appears in exactly half of all subsets (2^(n-1) subsets). So each element contributes to the final sum a fixed number of times, regardless of which subset it lands in. Once you realize that, the problem collapses into a single loop: sum up the elements, multiply by 2^(n-1), and you're done. The catch is that the backtracking approach is safer during an OA if you're unsure of the bit math. Either way, the topics here are Array, Backtracking, Bit Manipulation, and Combinatorics. If you haven't practiced subset enumeration or don't immediately see the XOR pattern, StealthCoder hedges the gap between 'I think I know this' and 'I'm shipping working code right now.'
Pattern tags
You know the problem.
Make sure you actually pass it.
Sum of All Subset XOR Totals recycles across companies for a reason. It's easy-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Made by a working Amazon engineer who got tired of watching qualified friends bomb OAs they'd solve cold in an IDE. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Sum of All Subset XOR Totals interview FAQ
Is the brute-force subset enumeration fast enough?+
Yes. With n up to ~12-15 elements in typical constraints, 2^n subsets is manageable. Backtracking through all subsets and computing XOR for each runs in O(2^n * n) time, which passes on every online assessment. The smarter mathematical approach is O(n), but both are accepted.
What's the mathematical trick everyone talks about?+
Each element appears in exactly 2^(n-1) subsets. So instead of enumerating every subset, you compute the sum of all elements once, then multiply by 2^(n-1). This converts an exponential enumeration into a linear calculation. It's clever but not required to pass.
Is this still asked by Microsoft?+
Yes, it's in their problem pool. It's an easy tag, so it typically appears as a warm-up or early problem in a loop rather than as the hard blocker. The 90% acceptance rate reflects that most candidates either know subset patterns or figure it out under time pressure.
How does backtracking relate to the other topics here?+
Backtracking is the vehicle for enumeration. Array is your input. Bit Manipulation applies to XOR operations. Combinatorics is the underlying math: you're counting subsets. The problem ties all six topics together in one small package.
What's the most common mistake during an OA?+
Forgetting to initialize the running XOR correctly or mishandling the base case in backtracking. Some candidates also compute XOR of the whole array once and think that's the answer, when the problem asks for the sum of XOR totals across all subsets. A clear walkthrough on a small example catches this fast.
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