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A riddle my math teacher asked back in 10th grade:

I am a fruit. If you take away the first letter of my name I become a crime. Take away the first two letters of my name I become an animal. Take away the first and last letter of my name and I become a form of music. What am I?

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    $\begingroup$ Very suitable joke for a teacher to tell 15 year olds... $\endgroup$ – IlludiumPu36 Oct 15 at 7:51
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You are a:

GRAPE

If you take away the first letter of my name I become a crime.

Removing the 'G' gives RAPE (though I have to be honest, using this serious word frivolously in a riddle makes me uncomfortable - you could perhaps clue this using the crop instead...)

Take away the first two letters of my name I become an animal.

Removing 'GR' gives APE.

Take away the first and last letter of my name and I become a form of music.

Removing 'G' and 'E' gives RAP.

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    $\begingroup$ The serious word you are talking about is the name of a place in Sussex, England - and it can be used as a metaphor, such as "the rape of the natural world", as well as the plant you mention.... regardless, I think we should disassociate the word from the vile act when playing word games or puzzles that involve words - same should apply for words like murder and torture - it is the act that should be abhorred, not the word itself $\endgroup$ – Jimmery Oct 15 at 15:20
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    $\begingroup$ Thanks for your thoughts @Jimmery. While I agree to an extent about dissociation I also have to respectfully disagree a bit (which I'm sure you won't mind). I don't feel we should try to normalise this word in a casual, flippant context. While (still very serious) crimes like murder might have been more commonly de-sensitised to a publicly accepted level for many centuries now (enabling the entire murder mystery genre, for example) crimes of a sexual nature are still considered very personally distressing for victims. Personally I just feel if it can be avoided in a puzzle, it should be... $\endgroup$ – Stiv Oct 15 at 15:55
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    $\begingroup$ @Stiv So rape is a more serious or egregious crime than murder? I don't follow your logic at all here, I guess that's why you say "I feel" a lot. I feel like you're making an absurd exception to disassociation of a word on an arbitrary interpretation of current social norms without concern for the long term effect it has on society. Rape as a word shouldn't be shied away from, nor should calling it a crime in a riddle... It's a horrid thing, but hiding in fear of a word, come on. $\endgroup$ – TCooper Oct 15 at 23:42
  • $\begingroup$ @Stiv I understand your aversion to the word - however I would caution against avoiding issues that we find unpleasant or abhorrent - taboo issues often continue regardless, albeit without the public attention required to mitigate or eliminate the issue itself - however this is a discussion best had on another forum $\endgroup$ – Jimmery Oct 16 at 8:17
  • $\begingroup$ @Jimmery Re 'another forum', agreed. It's a very valid discussion to have, but yes here in a comments thread on a puzzle is not the best place. Thanks for engaging - I take your point, even if we do approach this from different angles. To other (or future) commenters: I shall not be commenting further on this topic here on this thread; if you wish to discuss puzzle-related themes further with other members of this community, consider posting in meta or chat. Thanks. $\endgroup$ – Stiv Oct 16 at 8:27
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I am a fruit.

Grape

If you take away the first letter of my name I become a crime.

Rape

Take away the first two letters of my name I become an animal.

Ape

Take away the first and last letter of my name and I become a form of music.

Rap

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