Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 179
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In front of Leopold the cat has five mouse burrows, arranged in a row. There is a mouse hiding in one of them. Leopold can stick his paw into any of the burrows and try to catch the mouse. The mouse is afraid of the cat and after each try it will move to the next den on the right or on the left. In what minimum number of attempts can the cat be guaranteed to catch the mouse? A proof of the minima is not needed.
Is there a solution?
You have one litre of hot coffee (t=95 °C), one litre of cold tea (t=5 °C) and a set of vessels of different sizes. Is it possible, by heating one liquid with another and without using any other heat/cold sources, to make the final temperature of all tea higher than the final temperature of all coffee? The heat capacity of the vessels and the heat loss to the environment are neglected.
Lehko
Once upon a time there lived a homeless man in a basement among other homeless men like him. He collected 10 steers. He uses three of them to make a joint and smokes it. Question: How many cigarettes does the bum smoke?
Mathemat:
TheXpert:Перед котом Леопольдом пять мышиных норок, расположенных в ряд. В одной из них спряталась мышка. Леопольд может засунуть лапу в любую из норок и попробовать поймать мышку. Мышка боится кота, поэтому после каждой его попытки обязательно перебегает в соседнюю норку справа или слева. За какое минимальное количество попыток кот сможет гарантированно поймать мышку? Доказательство минимальности не требуется.
Surely there is a solution?
is the answer right?
All right!
Do you think with options 2,2,3,3,4,4 the mouse will still have a chance of not being caught? !
I'm sure she has a chance. Here's what it is:
She sits in 4 you in 2 she in 3, then you again in 2 and she runs to 2 after you. And then she runs from 1 to 2 and back
2234432
If Leopold the Artilleryman checks in order 1,2,3,4,5,1,2,3,4,5... (not necessarily starting from the first trench)
then he is guaranteed to catch a mouse if he is not allowed to run from the 5th trench to the first one and vice versa. And if a mouse can't stay in one foxhole for 2 tries in a row...
No, Sanya.
Understand that with 1,2,3,4,5 the mouse can move towards 5 to 1 - and won't even be spotted by the cat.
Do you think that with 2,2,3,3,4,4 the mouse will still have a chance of not being caught? !
Of course it will, see above. We have to be smarter than that. Leopold is a very clever cat.
If we are talking about the volume of 1 litre, it is impossible to make a litre of tea hotter than a litre of coffee without expending additional energy.
The condition says it all. Exactly all tea and all coffee. Exactly, without additional sources of energy.
Never say never.
I did it, by the way. The problem, however, hasn't been checked yet, but I am 100% sure about the solution.
Surely there's a solution? [cat and mouse]
Lehko [tea and coffee]
4...) [hobo]
1. There is, there definitely is, it counts for me.
2. I believe I got it easy, too.
3. Think again, Andrei, more is possible!
the solution is definitely there. i can guarantee to catch the mouse in 9 moves.
is the answer correct?
It's already good. But you can do it in fewer moves.
2234432
Almost right. But I have even less!
No, it's not, Sanj.
Understand that at 1,2,3,4,5 a mouse can move towards 5 to 1 - and not even be seen by the cat.
cat 1,2,3
Mouse 5-4,4-3.
caught in 2 mouse and 3 cat moves
Cat 1,2,3,4,5,1,2,3
Mouse 2-1, (if not jumping from first to fifth) 1-2,2-3,3-4,4-5,5-4 (if not jumping from fifth to first),4-3
caught in 7 mouse moves
3. Think again, Andrei, more is possible!
Oh, * of course. The funny thing is that I came up with the right idea but managed to calculate it wrong.
/Edited by Mathemat/
Cat 1,2,3
Mouse 5-4,4-3
caught in 2 mouse moves and 3 cat moves
Cat 1,2,3
Mouse 2,1,2.
Got it?
Cat 1,2,3,4,5,1,2,3
Mouse 2-1, (if you don't jump from the first to the fifth) 1-2,2-3,3-4,4-5,5-4 (if you don't jump from the fifth to the first), 4-3.
caught in 7 mouse moves.Try to think more broadly, based on more general hypotheses. This is a clue, by the way.
From my comments you can see that the maximum moves are no more than 6.
Look: cat 1,2,3,4,5. Mouse 4,5,4,3,2, and after the last move, 1. See? The mouse went through the cat and the cat didn't see it.
Oh, * of course. the funniest thing is that I came up with the right and managed to calculate it wrong.
Look: cat 1,2,3,4,5. Mouse 4,5,4,3,2, and after the last move - in 1. See? The mouse went through the cat and the cat didn't see it.
Cat 1,2,3,4,5,1
Mouse 4-5,5-4,4-3,3-2,2-1
Passed, but the cat caught it, following its strategy, in order from 1 to 5 and back to 1.
The number of moves in this strategy depends on where the cat goes first and where the mouse was.