#11 - Math Prime number puzzle

If 'a' is a prime number, then prove, that a*a+26 is NOT a prime number (whether it is true).

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Showing that a*a+26 is not prime when a=3 is true but not a math. proof. However it is quite easy: (if I didn't misunderstand)
a*a + 26 =
a*a -1 + 27=
(a-1)*(a+1) + 27

Now, since a is prime, it can not be a mutliplier of 3. Then either (a+1) or (a-1) should be a multiplier of 3.
Then (a-1)*(a+1) is multiplier of 3
And (a-1)*(a+1) +27 is also multiplier of 3
Then it's not prime.

#12 - Mathematical Brain Teaser

By moving one of the following digits, make the equation correct. 62 - 63 = 1

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2^6 - 63 = 1

#13 - Sequence Puzzle

The below is a number puzzle. It should be read left to right, top to bottom.
Question 1 What is the next two rows of numbers.
Question 2 How was this reached.
1 1
2 1
1 2 1 1
1 1 1 2 2 1

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3 1 2 2 1 1
Ano, now to explain...
Ano, first, seperate the number sequence into groups of numbers based on what number they are, for example '1 1 1' '2 2' and '1'. Then, take the total number of numbers in the first group -there's 3 ones, so we use 3- and then put what number was counted -in this group, 1-, and repeat with the remaining numbers.
Ano, the next line would be '1 3 1 1 2 2 2 1', following the same process as above...

#14 - Mathematical Puzzle

What mathematical symbol can be placed between 5 and 9, to get a number greater than 5 and smaller than 9?

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A decimal point. (5.9)

#15 - 11april

Rearrange the letters in 'new door' to make one word. I will only accept 1 answer.

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new door = one word
New door is an anagram of one word!

#16 - Island Puzzle

There are people and strange monkeys on this island, and you can not tell who is who. 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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Conjunction used by A is true only if both parts are true. Under the assumption that B is an honest man, then A would be honest too (B says so) and so B would be a liar as A said, which would be a conflict. So B is a liar. And knowing that, B actually said that A is a liar, too. First statement of A is thus a lie and B is not a lying monkey. However, B is lying which means he is not a monkey. B is a lying man. The second statement of A indicates that A is a monkey – so A is a lying monkey.

#17 - 7april

A man is stranded on an island covered in forest.

One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole
island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the man survive the fire? (There are no buckets or any other means to put out the fire)

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The man picks up a piece of wood and lights it from the fire on the west end of the island.

He then quickly carries it near the east end of he island and starts a new fire. The wind will cause that fire to burn out the eastern end and he can then shelter in the burnt area.

The man survives the fire, but dies of starvation, with all the food in the forest burnt..

#18 - The Ball Puzzle

How can you throw a ball as hard as you can and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.

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Throw the ball straight up in the air.

#19 - Roses Puzzle

I have a number of roses for sale. The first buyer bought half of my roses then I gave him additional one for free. The second buyer bought half of the remaining roses then I gave him additional one also for free. The third buyer also bought half of the remaining roses then I gave him additional one also for free, this time all of my roses has been sold out.

How many roses do I have?

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0+1 = 1
*2 = 2
+1 = 3
*2 = 6
+1 = 7
*2 = 14

14 roses

#20 - WHAT AM I Problem

The beginning of eternity. The end of time and space. The beginning of every end and the end of every place. What am I?

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The letter e