[BLANK_AUDIO] Sometimes we make mistakes. Sometimes we, we are wrong. And this happens even when we are in the mode of deduction. Even when there is real logic, sometimes we make mistakes. We're influenced by committee bias, by different reason. And I just have four little exercises, just to show this particular point. First question here. You have a chessboard. You just remove two little squares. Two little squares. You have 31 tiles and each tile is exactly the size of two square. My question is, is it possible to cover the whole chessboard with the tiles? You think yes, because, on one hand 62, and the other hand 62. There's no problem. You're wrong. Why? Look at the chess board. The two removed little square were white. If you take a tile and you put it on the chess board, wherever you want, it covers, necessarily, a little white and a little black. So, you cannot succeed because, on the chess board, you have 32 blacks and 30 whites. Not possible to do what I've asked. It's pure logic and maybe you were wrong. Next exercise. [BLANK_AUDIO] Here a product. I want you to give me the answer. How much is 2 times 3 times 4 times. Okay? You just remember what you have in your mind. Imagine, I have another question. How much is 8 times 7 times 6? Now, compare your two answers. Most probably, the first answer was a lower number. Because 2 times 3 times 4, 24. You go to, I don't know, 1500. With the other one, 8 times 7 times, maybe you are in the 5,000, I don't know. It shows that even if there is one right answer, the way you frame the question probably will lead you in one or in another direction. It's another good example. That, when you are in a hurry. And you think even logic can produce mistakes. Let's move to the next one. It's a bit more long. So, the situation is this one. Jack looks at Helen. And Helen looks at Charlie. Jack is married, and Charlie is not. The question, is there a married person looking at an unmarried person? Three options, yes, no, impossible to decide. Maybe you think you cannot answer, because there is an information missing. The status of Helen. You're wrong, the answer is yes. Why? Because there are only two possibilities. Either Helen is married or not. And in both case, you will have a married person looking at an unmarried person. So, the answer was yes. Another example. Third exercise. It's a famous one. It was introduced by Kahneman and Tversky who got the Nobel Price in economy a long time ago. Look at this, my daughter is studying philosophy and works for Greenpeace. Do you think, in the future, the probability is higher to have her in a bank or to have her in a bank and in a feminist association. [BLANK_AUDIO] Maybe you go for the second one. And of course, you're wrong. Because, if you studied probability a little bit, you know that a combined probability is always lower than the, one of two, of the two. Logic, sometimes, is difficult.