[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 372

New comment
 

The number of combinations of 6 by 3, i.e. 6!/3!/3! = 20.

The student makes up all the options on a piece of paper and then starts going through them, making sure not to forget to return all the locks to the initial position after making sure that the flat is unlocked. And this happens a maximum of 20 times.

And even after he opens it, he has to sneak into the flat to get his credit card and then return all the locks to their original position.

 
Mathemat >>:

Число сочетаний из 6 по 3, т.е. 6!/3!/3! = 20.

There may be more than one option.

1. Locks are rotated with change of state. I.e. if it was open - after turning it is closed and vice versa.

The total number of variants is 20, because the initial state is restorable.

2. The locks are turned without changing state. Then the side in which the lock is to be closed is important.

2а. -- all locks are the same (in principle) -- 2 options -- unscrew all locks to the left, check, then to the right, check.

2б. -- locks close in different directions. Here the number of options is 2^6(64) even though we know that exactly 3 locks are closed, as the original state cannot be restored.


If I were the professor, I would put 10 locks and choose variant 2b :)

 

And what do the exclamation marks after the numbers mean?

And if the lock can close with one or two turns of the key?

 
TheXpert >>:

Может быть несколько вариантов.

1. Замки проворачиваются со сменой состояния. Т.е. если был открыт -- после проворачивания закрыт и наоборот.

Yes, yes, that's how it is.
 
TheXpert >>:

2б. -- замки закрываются в разные стороны. Здесь количество вариантов 2^6 (64) несмотря на то, что мы знаем, что закрыто ровно 3 замка, т.к. изначальное состояние восстановить невозможно.

We know that. The student does not know that.
 

What's the answer, Svetik?

An exclamation mark after a number is a factorial sign.

 
Swetten >>:
Это мы знаем. Студент про это не знает.
Then in option (1) the answer is also 64. Or 63, if the student is sure that the door is originally locked.
 
Mathemat >>:

Какой ответ-то, Светик?

I don't know, I've been given the task myself.

Can you do it without factorials, on your fingers, within the limits of school education? :)

P.S. I graduated from a pedagogical institute, a primary and lower secondary school teacher, if memory serves me correctly.

 
Swetten >>:
Это мы знаем. Студент про это не знает.


and https://ru.wikipedia.org/wiki/Примориал#.D0.9E.D0.B1.D0.BE.D0.B1.D1.89.D0.B5.D0.BD.D0.B8.D1.8F doesn't know about it.

But he got caught on another one, he had some sausage in the fridge

So, as always, an "A" for ingenuity and an "F" in the subject.

-------------------------------------------------------------

People! The pike is finally here!

Everybody go fishing.

 
Mischek >>:

народ ! ЩУКА пошла наконец-то

Все на рыбалку

We have also had a pike, but this year is strange: the flood was weak and the fish have not come in much so far. But my youngest son and I have already had a successful trip to the pike: 1pc-3.2 kg, the second was only 2.3 kg. We are going to go grayling in a week, it's a great fishing trip too...!!
1...365366367368369370371372373374375376377378379...628
New comment