Solution:

43

Explanation:
Here is the thing. You can buy any number of wings that can be divided evenly by three except for three by using the combinations of boxes of 6 and boxes of 9. (You must use at most the box of 9 and then multiple boxes of 6). Now, if there is a number that can't be divided by 3, use a box of 20. After purchasing the box of 20, if the number that remains is divisible by 3, then you are good to go. On the other hand if it is not, you will have to use a second box of 20. And the remaining number will definitely be divisible by 3.

Thus if we calculate the largest number that can't be bought is the one that requires two 20 pieces boxes before the remainder can be thinned down to a number divisible by 3. We know that 3 is the number that can't be purchased and can evenly be divisible, the largest possible number of wings that can't be bought are:
3 + 20 + 20 = 43.

Solution:

1 2 3 4 5 6 and 7 8 6

Since summation of numbers 1-9(1 2 3 4 5 6 7 8 9) is 45 , so its impossible to divide into two equal parts.
Since we cant flip over 6 to make it 9 but we can flip 9 to make it 6 and hence the solution

Solution:

See the colored sticks in the picture. We have moved those sticks in the position given in the second image corresponding with the color.

Solution:

Karate Kid (car + at + tea + kid)

Solution:

Yes, you should switch the envelope. In the beginning when you picked up the envelope, you had a 1/3 probability of finding an offer letter in the envelope. There was 2/3 chance that the letter was there in the two envelopes on the table.

If you keep your selected envelope, you still have a 1/3 chance of finding an offer letter in that. However, since the interviewer has removed one empty envelope from the table, if you switch, you have a probability of 2/3 that the offer letter is inside that.

Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.

Solution:

Flyball should pay Lavy $11 instead of accepting his counter offer as in that case the club will end up paying almost double the amount.

Solution:

Slumdog Millionare = Slum + Dog + Million + air

Solution:

They used the planks in the manner that is shown in the figure.

Solution:

LOTTO

Explanation:
Just flip the two rows 1 and 2 vertically, you will find the word "Lotto".

Solution:

A) Fill 5 ml gallon ( 5mlGallon - 5, 3mlGallon - 0)
B) Transfer to 3 ml gallon (5mlGallon - 2, 3mlGallon - 3)
C) Empty 3 ml gallon ( 5mlGallon - 2, 3mlGallon - 0)
D) Transfer 2 ml from 5 ml gallon to 3 ml gallon (5mlGallon - 0, 3mlGallon - 2)
E) Fill 5 ml gallon(5mlGallon - 5, 3mlGallon - 2)
F) Transfer 1 ml from 5 ml gallon to 3 ml gallons(5mlGallon - 4, 3mlGallon - 3)