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In this paper we explore the effectiveness of solution of computationally intensive problems in FPGA (Field-Programmable Gate Array) on an example of Sudoku game. Three different Sudoku solvers have been fully implemented and tested on a low-cost FPGA of Xilinx Spartan-3E family. The first solver is only able to deal with simple puzzles with reasoning, i.e. without search. The second solver applies breadth-first search algorithm and therefore has virtually no limitation on the type of puzzles which are solvable. We prove that despite the serial nature of implemented backtracking search algorithms, parallelism can be used efficiently. Thus, the suggested third solver explores the possibility of parallel processing of search tree branches and boosts the performance of the second solver. The trade-offs of the designed solvers are analyzed, the results are compared to software and to other known implementations, and conclusions are drawn on how to improve the suggested architectures.