Re: Puzzler -- Toy Blocks
Response To:
Puzzler -- Toy Blocks ()

Larry Barrett
I started with 1 block, 1 step, 1 way - B
Then 3 blocks, 2 steps, 2 ways, - BBG and BGB
Then 6 blocks, 3 steps, 7 ways - BBBGGO, BBBGOG, BBGGOB, BBGOGB, BBGOBG, BGOBGB, BGOBBG. If I did this correctly I observe that after the first BBB, I can use the 2 step solution and abbreviate these two ways as BBB(2 step solutions), or BBB(2); also after the last two ways, which can be BGO(2). So the # ways for 3 steps can be shown as 2+1+1+1+2 = 7

Next is the 10 block, 4 step solution. Some of the ways make use of the abbreviation technique for the 3 steps solution and the 2 step solutions:
BBBB(7), BBB(7)B, BB(2)BGBG, BB(2)BBGG, BGOR(7), BGB(2)GORO, BGB(2)GOOR. Total # ways = 7+7+2+2+7+2+2 = 29.
Pretty complicated. Probably some way to use factorials.

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