How many words can a pen with half refill write?

A frog is at the bottom of a 30-meter well. Each day he summons enough energy for one 3-meter leap up the well. Exhausted, he then hangs there for the rest of the day. At night, while he is asleep, he slips 2 meters backwards. How many days does it take him to escape from the well?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

Chef Andrea has to light the kitchen stoves to open her restaurant for the day. There are three stoves in the kitchen: A glass stove, a brick stove, and a wood stove. She only has one match. Which does she light up first?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

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I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

what does this below rebus represent identXQQQQQME

I am lying and I always lie. Tell me whether I am lying or telling the truth.