Suppose we have 3 consecutive numbers A, B and C where A and C are prime.
Because A and C are primes they are also odd, if they were even they could be divided by two and wouldn’t be prime. This also means that B is even.
Suppose X is the largest multiple of 3 less than A. There could be two possibilities for A: A is X+1 or A is X+2. (If A is X+3, a could be divided by 3 and wouldn’t be prime)
If A is X+1 than B is X+2 and C is X+3. If C is X+3 it can be divided by 3 and wouldn’t be prime so A isn’t X+1.
Which means that A is X+2, B is X+3 and C is X+4. And if B is X+3, B can be divided by 3.
So B can be divided by 2 (even) and by 3, and any number that can be divided by 2 and by 3 can also be divided by 6.

The poison was in the ice cubes (on the rocks).
Jacob drank the scotch so fast the ice cubes didn’t have time to melt.
When John drank it a couple of minutes later enough ice with poison has melted in order to kill him.

115

Every time she fills a box with 8 smaller boxes the number of empty boxes increases by 7.
She has 102 empty boxes. Subtract the original 11 large and divide by 7 giving 13.
13 times she filled an empty box with 8 smaller boxes. So she uses 11 large boxes and 104 (13×8) other boxes (standard or small) giving 115 in total.

When we assume she fills all 8 standard boxes in a large box with small boxes than we can calculate the number of standard and small boxes used.
If she fills a large box with 8 standard boxes an each standard box with 8 small boxes she will have 64 empty small boxes.
If she does that twice she would have 128 small boxes but the total number of empty boxes is 102 so she does it only once.
In this case she would have used 11 large boxes 64 small boxes and 40 (=115-11-64) standard boxes.

6 is the minimum number of cuts.
If we focus on the biggest remaining block we get the following:

333 => 233 => 133 or 223 => 123 or 222 => 113 or 122 => 112 => 111

This is 6 cuts. It doesn’t matter how you arrange the smaller blocks.

The balloon will move to the front of the car.
Because of the inertia the heavier air in the car will move to the back pushing the balloon to the front.

You cannot calculate the probability because you don’t know how many of the marbles are white and how many are black.
There is at least one white marble, but they could all be white.
When you know the amount of white marbles (w) then the probability is (w/100)^100.

Jacob also wins the second race because it will cost him less time to run 5 yards than it will cost John to run that 5 yard

You shouldn’t add $2 to the $12 they paid, but subtract it from the $12.
The originally the meal cost $15 but the owner lowered it to $10.
They paid $12: $10 for the meal and $2 for the waiter

n=1; just select the coin with denominations 1