Number of Ways to Wear Different Hats to Each Other
A hard-tier problem at 44% community acceptance, tagged with Array, Dynamic Programming, Bit Manipulation. Reported in interviews at Mindtickle and 0 others.
You've got a problem that looks deceptively simple: people, hats, and the constraint that each person gets exactly one hat and no two people wear the same hat. Sounds like a basic assignment problem until you realize the trick is assigning hats to people, not people to hats. This hard-rated DP problem flips the typical approach and forces you into bitmask territory. Acceptance rate sits at 44 percent. If you hit this on your live OA and the standard DP recurrence isn't clicking, StealthCoder runs invisibly and surfaces the working bitmask solution in seconds.
Companies that ask "Number of Ways to Wear Different Hats to Each Other"
Number of Ways to Wear Different Hats to Each Other 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 FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know.
Get StealthCoderThe trap is thinking person-first: 'iterate through people, assign hats.' Wrong order. The insight is hat-first iteration combined with bitmask DP to track which people have already been assigned. You define dp(hat_index, people_mask) as the number of ways to assign hats starting from hat_index to the people represented by people_mask. For each hat, you try assigning it to each unassigned person whose size matches. Bit manipulation lets you toggle and check the mask in constant time. Without this reframing, you'll either overcomplicate the state space or miss pruning entirely. Common failure is confusing the order of iteration or mishandling the bitmask transitions. When you're stuck on the live assessment and the person-first approach isn't working, StealthCoder decodes the hat-first bitmask pattern instantly.
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Number of Ways to Wear Different Hats to Each Other recycles across companies for a reason. It's hard-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 FAANG engineer who treats the OA the way companies treat hiring: as a game with rules you should know. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Number of Ways to Wear Different Hats to Each Other interview FAQ
Why is the obvious person-first DP approach wrong here?+
Assigning people to hats one person at a time creates an explosion of invalid states. Reversing it, assigning hats to people, lets you skip hats with no matches and prune early. The bitmask tracks which people are still available, keeping state compact and pruning efficient.
Is this really asked at FAANG or just niche companies?+
Input data shows Mindtickle as the only reported company. It's a hard problem with lower frequency in public reports, which makes it a blind-spot problem. If you haven't drilled bitmask DP, this one will sink you fast on a live OA.
How does bit manipulation actually speed this up?+
Toggling and checking which person is already assigned takes O(1) with bitwise operations instead of O(n) with set or list lookups. On a problem with up to 10 people, a bitmask is 10 bits. Checking and updating the mask happens in a single CPU instruction.
What's the difference between this and the classic assignment problem?+
Classic assignment assumes a fixed matrix of costs. This problem's constraint is size: each hat fits only certain people. The hat-first, bitmask-tracked approach exploits that sparsity. Person-first DP doesn't naturally handle the size constraint without redundant states.
What's the actual time complexity and does it matter for interview?+
O(n * 2^n * m) where n is people count and m is hats. With n up to 10, 2^10 is 1024, so it's tractable. You need to know this scales to roughly 10 people max and explain why bitmask DP is the only sane approach for that constraint.
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