What is both possible and impossible at the same time?

Can you count the number of triangles inside a triangle?

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

What does the below rebus puzzle mean?

What does man love more than life, hate more than death or mortal strife; That which contented men desire; the poor have, the rich require; the miser spends, the spendthrift saves, and all men carry to their graves?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

Remove two matchsticks to make the below equation correct.

As shown in the image, the nine Dogs are square fenced. By constructing just two square fences can you make sure that two Dogs cannot meet each other without crossing the fence?

I am a white box having no key or lid.
Yet there is a golden treasure inside it.

What Am I?

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?