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Asked by fantasylan in Puzzles & Riddles, Miscellaneous Programming
Hi, I recently got this question as an interview question and I have been racking my brains to solve it. I tried coming up with some sort of formula/algo to do it but then I figured out I am better of using dynamic programming in C#/Java. The problem being I have not done this kind of thing before and I dont know how to start. The question is as follows. Any help will be highly appreciated.
Suppose you want to build a solid panel out of rows of 4×1 and 6×1 Lego blocks. For structural strength, the spaces between the blocks must never line up in adjacent rows. As an example, the 18×3 panel shown below is not acceptable, because the spaces between the blocks in the top two rows line up (shown by the dotted line).
There are 2 ways to build a 10×1 panel, 2 ways to build a 10×2 panel, 8 ways to build an 18×3 panel, and 7958 ways to build a 36×5 panel.
How many different ways are there to build a 64×10 panel? The answer will fit in a 64-bit signed integer.
20091028-EE-VQP-88 - Hierarchy / EE_QW_3_20080625
