How can you write nineteen in a manner that if we take out one, it becomes twenty?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?

I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

Jack looks at the 4 cards i gave him, and says out loud which card Joseph is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Jack needs to know is the order of the cards and what is on their face, nothing more.

Can you place three balls such that the equation shown in the picture holds true?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

With the help clues provided in the image, can you find the 5 digit key?

Jim and Sarah are in a long-distance relationship. Jim buys an engagement ring for Sarah and wants to mail it to her. Unfortunately, the only way to ensure the ring will be received is to place a lock on the package. Jim has locks and Sarah has locks, but neither has keys for each other’s locks. How can they make sure the ring isn’t stolen?

What is the last thing you take off before bed?

In the given picture, in how many ways can you read the word "Tiger"?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?