Spot what is wrong here in below Picture?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

Jenifer and Jesica are having a conversation.

Jenifer: I am definitely not over 30.
Jesica: I am 28 and you are surely 5 years older to me at least.
Jenifer: No, you are at least 29.

You are told that both of them are lying throughout in the conversation. Can you find their respective ages?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

A plane crashed between the border of Mexico and America. Where do you bury the survivors?

You have to put a letter on the following to make it a meaningful word. The only challenge is that you can't use 'E'.

S E Q U E N C _

What has a bottom at the top?

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?