Sum of Squares

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?




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There is a river to cross using a river raft and there are eight people (father, mother, policeman, thief, 2 daughters and 2 sons). No one knows to operate the raft except the adults and also excluding the thief. Only two people can go in the raft at a time. The raft should keep coming back and forth in order to pick and drop the people.
Rules to be followed:
Father: the father cannot stay in the raft or outside the raft without the presence of the mother.
Mother: the mother cannot stay in the raft or outside the rat without the presence of the father.
Thief: the thief is not allowed to stay with any of the family members unless there is a policeman.
Policeman: the policeman can travel with anyone.
2 sons and 2 daughters: they are not allowed to travel in the raft without the presence of an adult. They cannot either travel in the presence of only thieves without the policeman. The sons cannot be with their mothers without their father's supervision. The daughters are not allowed to be there with their fathers without the supervision of their mothers. But the daughters and the sons can be left unsupervised (as long as the other rules are applied).
What is the sequence that the people should follow in order to cross the river through the raft keeping in mind all the rules?
The rules are applicable not only in the raft but also outside the raft.

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Is the statement valid that it does not matter how much older a sibling is, eventually the younger one will be half as old as the older one?

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By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

Matchsticks Equation

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Can you identify the direction in which this bus is moving; left or right?

Hint: The bus is moving on the roads of London.


Find Bus Direction

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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?

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What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

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Challenging

There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.