What would be the lowest score with 9 strikes and no gutter...

Which is pretty lousy for that many strikes, but better than any game I’ve ever bowled. I don't see how you could get a lower score under the specified parameters, since any rearrangement would result in more turkeys than just the one in the last frame.

X X 11 X X 11 X X 11 XXX

My first pass results in 135:

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What would be the lowest score with 9 strikes and no gutter balls?

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