Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 102
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// I solved it, by the way.
Ay mala! Don't write me the solution, I'll solve it myself - if others don't make it sooner.
P.S. There seems to be a glimmer that looks like a solution. Something with parity? Below is a spoiler (hint to be highlighted for a sneak peek).
The mouse, moving to the next cube, changes the parity of the sum of coordinates each time. So to pass all the cube except for the central one, it has to change parity 25 times - and alternately. This is where the cat is hidden, it seems to me. So changing parity from even to odd is about the same number of times as changing parity from odd to even (max difference is 1). I can't figure out the rest yet.
(5) A mouse chews a piece of cheese consisting of 27 cubes (like a Rubik's cube). As he eats one cube, he sequentially moves to one of its neighbouring cubes. Will she be able to eat all the cubes except the central one?
My mouse can't do that.
So is mine. By the way, the weight of the problem is 4.
P.S. This is another logical problem which has not yet been solved (or hinted at) here:
(4) What is the smallest number of squares of the 5×5 square to be painted so that any 3×3 square which is its part has exactly 4 painted squares? Prove that this number is minimal.
Mathemat:
Below is a spoiler (a hint to be highlighted in order to peek).
(Can we ask the MQ web developers to add a "spoiler" style to the editor?)
You can ask, but it will only be necessary for one branch...
Why? Spoiler alert is convenient to quote.
So, the cart challenge: it's not that simple. Friction contributes a role, ambiguously.
I remember ZExpert The Xpert saying that when snow is dumped orthogonal to the movement, some kind of impulse is given to the snow, which brakes the cart, because the MM, which is dumping it, pushes it against the movement.
So it turns out that you have to compare two things - the increased friction of the lazy one and the reverse (reactive) momentum of the working one. And everything is not obvious. Who needs it, I can remind you of the problem.
I remember ZExpert The Xpert saying that when snow is dumped orthogonal to the movement, some sort of momentum is given to the snow, which brakes the cart, as the MM that is dumping it pushes it against the movement.
I don't remember him saying that.