Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 126

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Mathemat:

P.S. Did you solve the 53 problem?

Yeah, I missed a lot of options. You can already say how many :)
 
TheXpert: Yes, I've missed a lot of options. You can already say how many :)

The gardener could buy a maximum of 64 packs of products, and the problem is solved even for this case. This is a hint to the solution algorithm.

(4) Megamozg is in a dense forest, which occupies exactly 100 km2 in area. The shape of the forest is unknown, but the forest is solid, without glades. Megamogg wants to get out of the forest by walking the minimum possible distance. What minimum length (and shape) path guarantees that one will be able to find the border of the forest?

(5) Two players take turns naming a natural number - the value of an imaginary bargaining chip. It is necessary that the number can't be paid with the previously named coins. Prove that the game cannot be played indefinitely.
 

Alexey, happy birthday!

Happiness, health, prosperity, solving all urgent tasks in the best way possible :)

 
alexeymosc:

Alexey, happy birthday!

Happiness, health, prosperity, solving all urgent tasks in the best way possible :)

Thank you, namesake!
 
Mathemat:

(4) Megamogg is in a dense forest that covers exactly 100 km2 in area. The shape of the forest is unknown, but the forest is solid, without glades. Megamogg wants to get out of the forest by walking the minimum possible distance. What is the minimum length (and shape) of the path that guarantees that it will be able to find the border of the forest?

Walk 10 km in any direction, and if the border of the forest is not found along the way, turn right (or left) by 90 degrees and go on. The border of the forest after that will be at least 10 km later. So the megabrain will have travelled no more than 20 km.
Solution: {a=0...+00; b=0...+00; a*b=100; a+b=min;} a=10, b=10.

 
(5) Megamozg decided to lock the three prisoners in a straight corridor divided by five passages into six rooms, with a fat, mustachioed guard standing in each passage, leaning against one of the walls. Each time a prisoner moves from one room to another, the guard standing in that passage moves to the opposite wall and leans against it (if several prisoners move at the same time, the guard moves accordingly). If all guards lean on one wall, it will collapse and the guards will be released. Can Megamogg initially lean the guards and place the prisoners in such a way that they can never get out?

Comment: think of the rooms as wagons and the passages between them as vestibules, very flimsy.

 
DmitriyN:

Walk 10 km in either direction and if you do not encounter a forest boundary along the way, turn right (or left) by 90 degrees and keep walking. The border of the forest after that will be at least 10 km later. So the megabrain will have travelled no more than 20 km.
Solution: {a=0...+00; b=0...+00; a*b=100; a+b=min;} a=10, b=10.

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Alexey, father invites you for mushrooms (white, mayberry, aspenberries and rudders) in threes. We have two navigators :)))

No way, nowhere does it say that the forest is square. it could be shaped like a letter g, and you'll be walking for a very long time the second 10 km
 
DmitriyN: Go 10 km in either direction, if you don't encounter a forest boundary along the way, turn right (or left) by 90 degrees and go on. The border of the forest after that will be no later than in 10 km. So the megabrain will have travelled no more than 20 km. Solution: {a=0...+00; b=0...+00; a*b=100; a+b=min;} a=10, b=10. ...

I like the logarithmic spiral better, but with what parameters I don't know yet.

 
GaryKa:
I prefer the logarithmic spiral, but I don't know what the parameters are yet.
In fact, there are probably only two options, either a spiral or a straight line
 
Mischek:
In fact, there are probably only two options, either a spiral or a straight line.
Although no, neither straight nor spiral, a forest can be either spiral or straight. You should probably use some kind of self-intersecting curve to cut off areas, i.e. use the fact that the forest is solid, without glades.
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