A professor thinks of two numbers

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?




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10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

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Find the next number in the series?
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There is a jar in which there are two types of candies.
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Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

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Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

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Olivia got the drink with the same letter as the one in her first name.
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Jigsaw puzzles

Jigsaw puzzles soared in popularity during the great depression, as they provided a cheap, long-lasting, recyclable form of entertainment.