Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

What is more useful when it is broken?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

I’m tall when I’m young, and I’m short when I’m old. What am I?

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?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

Known by all without exception, Forever here, for your protection, Sometimes strong, sometimes weak, Right after the night I come - hot and chic. And while millions of miles away, I always get to you, I find my way. No life around could do without me, Can you guess what I might be?

If I remove one from eleven it becomes Ten and if I remove one from nine also becomes Ten. How?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?