Required Mathematical Intelligence

Chapter 67 Two Clever Friends

Foreman Fidel has two clever friends: Mr. S and Mr. P.

One day, Fidel wanted to test them, so he took out 11 screws of each specification from the shelf, and placed them on the table in the following order:

M8×10M8×20
M10×25M10×30M10×35
M12 × 30
M14 × 40
M16×30M16×40M16×45
M18 × 40
What needs to be explained here is: the number after the M indicates the diameter, and the number after the X sign indicates the length.

After setting them up, he called Mr. S and Mr. P to him and told them:

"I will tell you the diameter and length of the screw I need, and see if any of you can tell the specification of this screw."

Then, he quietly told Mr. S the diameter of the screw and Mr. P the length.

Mr. S and Mr. P were silent for a while at the table.

Mr. S said: "I don't know the specification of this screw."

Mr. P also said: "I don't know the specification of this screw either."

Then Mr. S said: "Now I know the specification of this screw."

Mr. P also said: "I also know."

Then, they all wrote a specification on their hands to show Foreman Fidel.Foreman Fidel smiled happily after reading it. It turned out that the specifications written by the two of them were exactly the same, and this was exactly the one he needed.

Q: What is the specification of this screw?
[Answer: For the clever Mr. S, under what conditions will he say "I don't know the specification of this screw?" Obviously, this screw cannot be M12×30, M14×40, M18×40. Because there is only one screw with these three diameters, if the screw is M12×30, or M14×40, or M18×40, Mr. S, who is smart and knows the diameter of the screw, will immediately say that he knows it.

同样的道理，对于聪明的P先生来说，在什么条件下，才会说我也不知道这只螺丝的规格显然，这只螺丝不可能是M8×10、M8×20、M10×25、M10×35、M16×45.因为这五种长度规格的螺丝各只有一只。

这样，我们可以从11只螺丝中排除了8只，留下的是三种可能性：M10×30、M16×30、M16×40.
Next, it can be deduced according to Mr. S's sentence "Now I know the specification of this screw".Expressed in the form of inference: if the screw is M16×30 or M16×40, then Mr. S who only knows the diameter of the screw cannot determine the specification of the screw. However, Mr. S knows the specification of the screw, so , this screw must be M10×30.]
(End of this chapter)