A swan sits at the center of a perfectly circular lake. At an edge of the lake stands a ravenous monster waiting to devour the swan. The monster can not enter the water, but it will run around the circumference of the lake to try to catch the swan as soon as it reaches the shore. The monster moves at 4 times the speed of the swan, and it will always move in the direction along the shore that brings it closer to the swan the quickest. Both the swan and the the monster can change directions in an instant.
The swan knows that if it can reach the lake's shore without the monster right on top of it, it can instantly escape into the surrounding forest.

How can the swan successfully escape?

You’re out on the water and see a boat filled with people. You look away for a second and look back again, but this time you don’t see a single person on the boat. Why? Hint: The boat did not sink.

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?

The host of a game show offers the guest a choice of three doors. Behind one is an expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

John was gifted a new Hayabusa. He drove x miles at 55mph. Then he drove x+20 miles at 40mps. He drove his bike for 100 minutes. How much distance did he travel?

Can you spot the hidden girl in the picture below?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?