The magic word here is "calisthenics". These are the exercises like pushups, situps, etc.
Here are my personal favorite ones for core.
1. Flutter kicks
2. Bicycle Kicks
3. Side Planks
4. Russian Twist
Remember: you can do these core exercises all day, but it won't give you a six-pack. Cardio does that that.
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"When I get hold of the big bad wolf
I just push him under to drown
Then I bite him in a million bits
And I gobble him right down"
-Animal Crackers in My Soup by Shirley Temple... brutal