The Prime Numbers below 75

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?




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There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

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He runs but never walks. Murmurs, but never talks. Has a bed, but never sleeps. And has a mouth, but never eats?

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A man was telling some of his war stories to his grandchildren.
"When the World War I was on the verge of end, I was awarded for my bravery for I had saved a group of my men." He coughed and then added, "When we were fighting in northern France, an enemy soldier threw a grenade at us. Before it could explode, I picked it up and threw it away. For my act of bravery, right before the war ended, A General gave me a sword engraved with the words "Awarded for Display of Bravery and Heroism in World War 1"."

Hearing this, one of the grandson spoke up. "Grandpa, this is not a true story. It can"t be true!"

The truth is that it was not. How did the grand children know it?

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The person who makes it has no need for it; the person who buys it has no use for it. The person who uses it can neither see nor feel it. What is it?

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Can you fill the blank with the correct number?

6 30 870 756030 _____

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Place the numbers from 1 to 9 in the circles in a manner that each side of the triangle sums up to 17.

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A B C D E F G H

These are the letters given to you. Now you have to find out the letter that comes two to the right of the letter which is immediately to the left of the letter that comes three to the right of the letter that comes midway between the letter two to the left of the letter C and the letter immediately to the right of the letter F.

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A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

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I have an eye but still cannot see.

Who am I?

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