Answer: 301 eggs. The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1. For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.

Answer: Here are the two solutions. This is usually solved with guess and check although using logic may be faster. We know that each queen must be in it's own row vertically and horizontally. We also know that 4 of the queens must be on white and 4 on black. This is true because with 4 queens on the same color all of the rest of that color is venerable to attack. (It could be done with math).

Answer: The gravedigger, for his houses will last forever (he says until Doomsday).

Answer: All of the men (n) who are cheating will be killed and it will take one less than the number of cheating men nights (n-1) for their wives to discover this.

If one man was cheating, and that woman hadn't have heard of any other infidelity she would know it was her husband that was cheating. If there was two men cheating, both of their wives would think that since they have only heard of one man cheating he should die the next morning. If he doesn't die, she knows her husband must also be cheating and that's why the other husband didn't die. Following this logic, you can know that all of the men will die after one less night than there is cheating men.

Answer: Both cups end up having the same amount of the other liquid in it. When you take the spoonful of coffee (B) and put it in the tea (A) it increases the volume of the tea (A) by that spoonful. Then when you take a spoonful of the tea (A), part of that spoonful is coffee, taking away the proportional amount of coffee. This makes the amount of coffee in the tea and tea in the coffee equal.