Winnie has 45 cherry lollipops, 116 wintergreen lollipops, 4 grape lollipops, and 229 shrimp cocktail lollipops.  With no regard to flavor, Winnie gives each of her 11 nearest and dearest friends some lollipops.  Each friend gets the same number of lollipops and she hands out as many lollipops as possible.  How many lollipops does Winnie end up keeping for herself?
We want to know the remainder when $45+116+4+229$ is divided by 11.  The remainders of each of these numbers are easy to compute individually so we can say \[45+116+4+229\equiv1+6+4+9=20\equiv9\pmod{11}.\]Therefore Winnie has $\boxed{9}$ lollipops left over after the distribution.  Hopefully she did not keep any shrimp cocktails.
9
Level 2
Number Theory
Problem: Winnie has 45 cherry lollipops, 116 wintergreen lollipops, 4 grape lollipops, and 229 shrimp cocktail lollipops.  With no regard to flavor, Winnie gives each of her 11 nearest and dearest friends some lollipops.  Each friend gets the same number of lollipops and she hands out as many lollipops as possible.  How many lollipops does Winnie end up keeping for herself?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find out how many lollipops Winnie has in total, we need to sum the quantities of each flavor. The total number of lollipops is calculated as follows: 

45 (cherry) + 116 (wintergreen) + 4 (grape) + 229 (shrimp cocktail) = 394 lollipops.

Next, Winnie has 11 friends to whom she wants to distribute these lollipops equally. To determine how many lollipops each friend can receive, we need to divide the total number of lollipops by the number of friends:

394 lollipops ÷ 11 friends = 35 lollipops per friend with a remainder.

To find the exact number of lollipops distributed, we multiply the number of friends by the number of lollipops each receives:

11 friends × 35 lollipops = 385 lollipops distributed.

Now, we need to calculate how many lollipops Winnie keeps for herself. This is done by subtracting the number of lollipops distributed from the total number of lollipops:

394 total lollipops - 385 lollipops distributed = 9 lollipops remaining.

Thus, the final answer is 9.<|END_OF_LATENT|> The final answer is $9$.