Can you solve the photo plexer logic ?

Using Only Five 5's and any mathematical operator make sum as 37

Find the next number in the series below

21 32 54 87 131 ?

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

Why 1729 is a magic number? Answer Logically.

I make two people out of one. What am I?

The King of a distant land had heard that Birbal was one of the wisest men in the East and so desired to meet Birbal. He sent Birbal an invitation to visit his country.

In due course, Birbal arrived in the distant kingdom. When he entered the palace he was flabbergasted to find not one but six kings seated there. All looked alike. All were dressed in kingly robes. Who was the real king?

The very next moment he got his answer. Confidently, he approached the king and bowed to him.

How did Birbal know who was the real king?

Can you divide the below-given shape into four equal and identical pieces?