We are going with a collaboration of two minds between the friend


and a server;

in which exact mathematics and creative mathematics that is almost always recreational are in action.

And we will complement with a creativity exercise without numbers.


a What is missing and what is left over to your enemy to become your friend?

b 220 and 284 are friendly numbers, Find at least two evil numbers.

If you find them all in that range you will be congratulated

I remind you that a number is evil, when its binary expression has an even quantity of 1.

c Who is more courteous?

Man or woman?

d Prove that if you subtract the sum of its digits from any natural number greater than 9, you will get a number that is a multiple of 9.


If you had to change the ending of the fable “The Frog and the Scorpion”, what ending would you suggest?

The Fable: “The Frog and the Scorpion” says:

Once on the bank of a river, a Scorpion was disconsolate because he wanted to cross to the other bank.

A Frog that was passing by saw the Scorpion sad and approaching to know that she was afflicting him, asked him about his dilemma. 

The Scorpion told the Frog that he wanted to cross the river, but that he had no way of doing it since it was impossible for him.

Hearing this, the Frog decided to help him cross the river on the condition that he not do it for a year.

The grateful Scorpion accepted.

Thus, the Scorpion and the Frog were crossing the river, but halfway, the Frog felt the Scorpion's sting on his back and how the poison took effect making him fall asleep.

Before fainting, the Frog turned her head and said to the traitor:

"How is it possible?! You said you wouldn't hurt me, now because of you we'll both drown!"

The Scorpion promptly replied:

"I'm so sorry Rana, I can't help what I am. This is in my nature."

Remember that:

“An insignificant solution out of your own head is preferable;

than a great one copied on the Internet or from another, especially without understanding it”.


Hands and mind to work!