Number of Valid Move Combinations On Chessboard
A hard-tier problem at 48% community acceptance, tagged with Array, String, Backtracking. Reported in interviews at PayPal and 0 others.
You're staring at a chessboard with a knight and a bishop, and the problem asks you to count valid move sequences. This is a hard problem that PayPal has asked, and it combines backtracking, simulation, and careful state tracking. The acceptance rate is 47 percent, which means half the candidates who attempt it get stuck on either the move generation, the board boundary logic, or the backtracking structure itself. If this problem hits your live OA and you blank on how to structure the recursion or handle piece collisions, StealthCoder solves it in seconds, invisible to the proctor.
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Number of Valid Move Combinations On Chessboard 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. Built because the OA filter rejects engineers who'd pass the on-site. That's a broken filter. This is the workaround.
Get StealthCoderThe core trick here is recognizing that you need to simulate both a knight and a bishop moving on the same board, and count every valid sequence of moves that doesn't leave either piece in check or off the board. The obvious mistake is treating this like a standard permutation problem. You can't just generate all possible move sequences and filter; you have to use backtracking to prune invalid states early. The real complexity is threefold: tracking two piece positions simultaneously, checking if either piece is in check after every single move (which requires understanding attack patterns), and ensuring pieces don't capture each other. Most candidates either skip the check validation or fail to properly combine the state of both pieces. This is where the Array and String topics come in; you're likely using arrays to represent the board and strings to encode positions. StealthCoder is the hedge for the one problem where the state-space explosion catches you off guard and you run out of time to code the full solution.
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Number of Valid Move Combinations On Chessboard 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. Built because the OA filter rejects engineers who'd pass the on-site. That's a broken filter. This is the workaround. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Number of Valid Move Combinations On Chessboard interview FAQ
How do I know if a knight or bishop is under attack?+
You need to simulate every possible attack square for the opponent piece after each move. For a knight, that's 8 potential L-shaped moves. For a bishop, that's all diagonal squares until board edge or collision. Both must be checked after every single move in your backtracking, which is why this problem is hard and expensive.
Is this really asked at companies like PayPal?+
Yes, PayPal has asked it. It's a low-frequency hard problem overall, but it shows up in roles requiring strong backtracking and simulation chops. If you see it, you're likely being tested on your ability to handle complex state and performance under pressure.
What's the difference between this and a standard N-queens backtracking problem?+
N-queens fixes pieces on the board and checks columns/diagonals once. Here, pieces move repeatedly, so you have to validate the board state after every transition. The state space is much larger and the validation is continuous, not static.
How do I structure the backtracking base case?+
Your base case should trigger when both pieces have no valid moves left. That means after each move, you check if the current player's piece can move anywhere without putting itself or the other piece in a bad position. If neither piece can move, you've found a valid sequence.
Will I get TLE if I'm not careful?+
Yes, state explosion is real. You need to prune aggressively; stop exploring a branch as soon as a piece is in check or a move is invalid. Memoization of board states can help, but understanding what to prune first is critical to staying within time limits.
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