Domino and Chess

Can you cover the chess board with 31 domino pieces, such that only two opposite corners are left uncovered?

The answer is NO. Every domino piece covers exactly one black and one white square on the chess board. Since initially you start with different number of available white and black squares on the chess board, it is impossible to cover it with domino pieces.

Sequence 1, 11, 21

What follows next in the sequence below?

1, 11, 21, 1112, 3112, 211213, 312213, ?

Every term in the sequence describes how many 1s, 2s, 3s, etc. are there in the previous term. “11” means that in the previous term there is one 1. “21” means that in the previous term there are two 1s. “1112” means that in the previous term there is one 1 and one 2. “3112” means that in the previous term there are three 1s and one 2. “211213” means that in the previous term there are two 1s, one 2 and one 3. “312213” means that in the previous term there are three 1s, two 2s and one 3. Therefore the next number in the sequence should be 212223.

3 Men, 1 Woman

Warning: this puzzle involves sexual themes and may be inappropriate for younger audiences. If you are not mature, please skip this question.

They can start by putting the two condoms on top of each other and let the first man have sex with the woman. After that the second man can take out the inner condom and have sex with the woman using just the outer condom. Finally the third man can take the removed inner condom, turn it inside out and place it back in the outer condom. Then he can have sex with the woman using the two condoms simultaneously.

Tough Decisions

You are driving your car along the road in a very harsh snowy weather and reach a bus stop. On this bus stop you see that there are three people waiting – your best friend, a sick old lady and the girl of your dreams. The car unfortunately can accommodate only 2 people (including you), so you can not take all of them with you. What will be your choice?

The best solution is to let your friend drive the old lady and you stay with the girl of your dreams on the bus stop.

Optical Illusions

If you count carefully the number of people before the tiles scramble and after that, you will see that one person disappears. Can you explain how this is possible?

Similarly, on this picture it looks like after changing the places of the tiles on the diagram, their total area decreases by one. Can you explain this?

If you look carefully, you will notice that every person on the picture with 12 people is slightly taller than his corresponding person on the picture with 13 people. Basically, we can cut little pieces from 12 different people without making noticeable changes and arrange them into a new person.

For the second question, none of the shapes before and after the scrambling is really a triangle. One of them is a little bit curved in at the hypothenuse and at the other one is a little bit curved out. This is barely noticeable, because the red and the blue triangle have very similar proportions of their sides – 5/2 ~ 7/3.