See if you can figure out what these seven words all have in common?
1. Banana
2. Dresser
3. Grammar
4. Potato
5. Revive
6. Uneven
7. Assess

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Correct but not... specific enough for a gold star.

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Gold Star answer:
These words can each be changed to the same word written BACKWARDS, 
           by taking the first letter and putting it at the end:
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1. ananaB
2. resserD
3. rammarG
4. otatoP
5. eviveR
6. nevenU
7. ssessA

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So far this thread has 3 puzzles going that have not been answered all right, or completely:
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Which raindrops fall faster, the small ones or the large ones?  <--- (The OP)
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A baseball is tossed upwards into the air.
Which takes longer, its flight up or its drop back down?
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A large stone is 100 times heavier than a small rock, but when dropped at the same time, they fall with the same acceleration (ignoring air resistance). Why doesn't the large stone accelerate faster? Is it because of its weight, its energy, its surface area or its inertia?
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I'd be glad to post my solutions but I don't want to spoil anyone's fun!
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In the meantime, here's another one!  
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CORK IN A GLASS                                                       ...btw a refutation of flat-earthers' canard that "water does not bend"...
You have no doubt observed that a cork will always drift over to the side of a water glass and stay there. Can you think of a way to make the cork float in the middle of the glass without touching either the cork or the glass?
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Regarding this last one, if you don't have a cork, that's no problem. All you need is a glass of water and a metal or plastic bottle cap (like the one from your last bottle of beer or soda or filtered water). With the glass less than full, so you can see the surface of the water reflecting a light beyond the glass, place the bottle cap into the glass of water, carefully, so as to not let any water get into the cap. Then stand still and watch. The cap will slowly drift to the side of the glass. Notice as it approaches the glass wall, the cap ACCELERATES. This is very important to see happening. You can try bumping the cap with a pencil or your finger to make it stay in the center if you want to experiment, but to solve the puzzle you can't be touching the cap with anything like that. There is another answer and it is DEFINITIVE about the curvature of the surface of water like this.

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Regarding the second puzzle, the baseball, there is another thread here where I posted a copy of a US Navy declassified bulletin that describes the muzzle velocity and velocity at impact of 16" artillery shells for many various ranges (distances). With a muzzle velocity of 2500 fps, the Striking velocity for range of 19,800 yards is 1745 fps., a loss of 30%. However, the "Striking velocity" (column 5) for half that range (9,900 yards) is 2078 fps., a loss of only 17% (more than half the loss of the longer range). This is the case with all the Striking velocities in the charts. The velocity loss is always greatest from the start, and gradually decreases with range. Elsewhere the bulletin confirms that the projectiles are continually affected in flight by air resistance, which accounts for this slowing effect. They even provide adjustment factors for cross wind, tail wind, head wind, and any combination thereof. 
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Consequently, the baseball puzzle can't be any different, in that the ball faces air resistance when the ball is moving, and that resistance causes the ball's kinetic energy to be dissipated in some degree, both on the way up (loss is more rapid when the ball is moving faster), and on the way back down (less loss due to air resistance coming down), similar to the trajectory of these 16-inch shells, and approximately like the difference between a range of 19,800 and 9,900 as if the latter were halfway up for the baseball, and the former applies to the baseball's entire flight up and back down again.
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Gee, that's special. Thank you, Nadir! Looks like a Texas star.
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See if you can figure out what these seven words all have in common?
1. Banana
2. Dresser
3. Grammar
4. Potato
5. Revive
6. Uneven
7. Assess

Stripping the first letter there remain palindromes:

anana
resser
rammar
otato
evive
neven
ssess

Oh, I was late. Congrats, Neil Obstat.

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Thank you, Struthio. For consolation, here is another opportunity for you!
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There are three mistakes in the following message; can you spot them all?
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1.) tree three
2.) mistake mistakes
3.) there are only two mistakes

But how come the answer lists three mistakes while number 3 says that there are only two?

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Bingo.  -- The original question states there are 3 mistakes, so that's a given. If the word "tree" were replaced with "two" then there would be 5 mistakes: the "r" "e" and "e" of "tree" would be 3 of them, the missing "h" is a fourth (the "t" is the only letter that is correct since it also occurs in "two"), and the missing "final s" for "mistake" makes 5. So changing "tree" to "three" by adding an "h" allows for fewer (fewer is better!) wrong letters than does changing "tree" to "two." Perhaps the original question should say there are at least 3 typos in the sentence. Also, it depends whether you want to think that each wrong letter counts as a mistake, or if two or more wrong letters occur in the same word, that's only good for one "mistake."

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What English word has all 6 vowels in order?
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What common word includes the letters "wsst"?

Neil, do these questions pertain to the same word?