Solution:

Let us assume,
the radius of the river is R.
the speed of beast is S.
the speed of duck is S/4.
Circumference = 2 * Pi * R.

Now, if duck swims R/4 distance from the center of the river and then begins to swim across the river in center implies both duck and beast can take the round trip in same time.
Explanation :
time by beast : 2 * Pi* R * S
time by duck : 2 * Pi* R/4 * S/4 => 2 * Pi* R * S


Now, the duck can move slowly inward toward the center of the river, and begin swimming around the center in a circle from this distance. It is now going around a very slightly smaller circle than it was a moment ago, and thus will be able to swim around this circle FASTER than the beast can run around the shore.

The duck can keep swimming around this way, pulling further away each second, until finally it is on the opposite side of its inner circle from where the beast is on the shore. At this point, the duck aims directly toward the closest shore and begins swimming that way. At this point, the duck has to swim [0.75R feet + 1 millimeter] to get to shore. Meanwhile, the beast will have to run R*pi feet (half the circumference of the river) to get to where the duck is headed.
The beast runs four times as fast as the duck, but you can see that it has more than four times as far to run:

[0.75R feet + 1 millimeter] * 4 < R*pi

[This math could actually be incorrect if R were very small, but, in that case, we could just say the duck swam inward even less than a millimeter and make the math work out correctly.]

Because the duck has less than a fourth of the distance to travel as the beast, it will reach the shore before the beast reaches where it is and successfully escape.

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:

Adam and Eve were the only people without navel. As they were not born out of a mother, they never had umbilical cords and thus never had navels.

Solution:

You better switch!

Your first choice has a 1/3 chance of having the car, and that does not change.<br>The other two doors HAD a combined chance of 2/3, but now a Goat has ben revealed behind one, all the 2/3 chance is with the other door.

Solution:

When you were inside the shed, the murderer replaced the lock with his own one that was identical to your original lock. When you locked the store room, you did not require a key and there was nothing abnormal for you. When you left, the murderer opened the lock with his key, planted the dead body inside and replaced the lock again putting the original lock in the place. He then closed it without any problem.

Solution:

The answer is 'R'

It represents the gear stick. The number 1-5 represents gears and the last one thus should be reverse i.e. R.

Solution:

He askes the god to beat him half to death.

Solution:

It can be done as shown in the picture below.

Solution:

Let m be initial number of flowers and n be the flowers offered at each temple by the man.
Initial flowers = m
After stepping into the first temple = 2m
Flowers offered at the first temple = n
Remaining flowers = 2m – n

After stepping into the second temple = 4m – 2n
Flowers offered at the second temple = n
Remaining flowers = 2m – n

After stepping into the third temple = 8m – 6n
Flowers offered at the third temple = n
Remaining flowers = 8m – 7n

Now as per the question (8m – 7n) must be equal to 0.
i.e. 8m – 7 n = 0
or 8m = 7y

Now the least numbers required to solve this equation are 7 and 8 for m and n respectively.

Thus m = 7; n = 8
Which means, the man had 7 flowers in the beginning and he offered 8 flowers at each temple.

Solution:

In the picture you can find the green matchsticks. We have moved them from the bottom and placed them in the middle. It was a bit tricky but now you have your desired result.

Solution:

Since each one of them gave one answer wrong, this means that each one of them gave two answers right.

Let us assume that Student A gave a wrong answer to the first question. This will mean that Student B also gave a wrong answer for the first. This will conclude that the rest of the two answers given by them are correct. However, the answers are different and thus it is not possible.

Thus both Student A and Student B must be right with the first question and the answer to the first is two.

If you keep applying the same logic, you will come to a conclusion that following are the correct answers:
Q1. Two
Q2. Three
Q3. Two