If ...., I then have to solve a riddle involving a fish and a rake.
What is the meaning of solve a riddle involving a fish and a rake in the above sentence?
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This is how dictionaries define the word rake: a rake is a gardening tool that consists of a pole with a toothed crossbar or fine tines at the end, used especially for drawing together cut grass or smoothing loose soil or gravel. Here's a picture of it:
The phrase to involve something means to have or include something as a necessary or integral part or result. Once again, I got all that information straight from a dictionary.
Finally, this is what that sentence fragment is saying:
I then have to solve a riddle (a puzzle) that includes (incorporates, contains, consists of) two things: a fish (the kind of fish that swims in water) and a rake.
I think that's as simple as you can possibly break this down.