Why is the longest human nose just 11 inches?

There is a unique number which when multiplied by any number from 1 to 6, we will get the new number that contains the same digits only.

Can you find that number?

How can you take 2 from 5 and leave 4?

Nodes are shown below and you need to connect them based on the following rule: Every node can be connected to the number of nodes inside them, i.e. the first node there is a value of 1 which indicates that the first node can connect to exactly one node only.Can you do it?

Can you find the next number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

You see me once in June, twice in November, and not at all in May. What am I?

What can jump higher than a building?

In a university, a professor gave a set of three problems to the three brilliant students of his class. See the image for the questions.