Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 129
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In this case, I think the distances will be the same, I don't see any good reason for them to be different. The unwound rubber washer has a slightly larger diameter, but I don't think this plays a significant role.
Also, the puck has a knurled surface around its circumference and is able to cut some roughness in the ice with this "file-like" surface, which does not play much of a role either.
Yes, the washer diameters are the same, and there is no destruction of the rubbing surfaces.
2 TheXpert: We're not talking about any STO. The usual classical mechanics, and the answer is very simple. It's just a matter of figuring it out.
Another one, but my own solution seems too simple:
(4) Find the smallest number from the set of all those natural numbers which cannot be defined by less than sixteen words.
And another one:
(4) In a Latin American country ruled by Megamoggle, it is time for a new election for the country's leader. There are exactly 100,000,000 eligible voters in the country. Only 1% of them support Megamozg. But Megamogg, in order to appear "democratic" in the eyes of the world public, wants to be "fairly elected". The voting procedure in this country is as follows: Megamozg divides all voters into a number of equal groups, then these groups into several more equal groups, and so on. In the smallest groups the people choose a delegate, then the elected electors choose the next delegate in the largest group and so on. At the end, the representatives of the largest groups of voters choose the leader of the country. The megabrain itself divides the population into groups. Can he hold an election so that he is "democratically" elected? (If the votes are equal, the opposition Occupy candidate wins).
(4) In a Latin American country ruled by Megamoggle, it is time for a new election for the country's leader. There are exactly 100,000,000 eligible voters in the country. Of these, only 1% support Megamozg. But Megamogg, in order to appear "democratic" in the eyes of the world public, wants to be "fairly elected". The voting procedure in this country is as follows: Megamozg divides all voters into a number of equal groups, then these groups into several more equal groups, and so on. In the smallest groups the people choose a delegate, then the elected electors choose the next delegate in the largest group and so on. At the end, the representatives of the largest groups of voters choose the leader of the country. The megabrain itself divides the population into groups. Can he hold an election so that he is "democratically" elected? (If the votes are equal, the opposition Occupy candidate wins).
The condition is Latinos. But, actually, it's very similar to the finks, too.
Important addendum: the elected candidate can vote (for himself, of course). Megamook knows in advance who is voting for whom.
(4) In a Latin American country ruled by Megamoggle, it is time for a new election for the country's leader. There are exactly 100,000,000 eligible voters in the country. Only 1% of them support Megamozg. But Megamogg, in order to appear "democratic" in the eyes of the world public, wants to be "fairly elected". The voting procedure in this country is as follows: Megamozg divides all voters into a number of equal groups, then these groups into several more equal groups, and so on. In the smallest groups the people choose a delegate, then the elected electors choose the next delegate in the largest group and so on. At the end, the representatives of the largest groups of voters choose the leader of the country. The megabrain itself divides the population into groups. Can he hold an election so that he is "democratically" elected? (If the votes are equal, the opposition Occupy candidate wins).
I have it that MegaMoscow needs only 531441 votes from his supporters to win, i.e. just over 0.53%.
Very close to the truth. "Close" not because it's inaccurate, but because I didn't calculate this number myself, but just showed the algorithm :)
In the comments to the problem it was also suggested to find the minimum percentage of supporters at which MM can win.
Very close to the truth. "Close" not because it's inaccurate, but because I didn't calculate this number myself, but just showed the algorithm :)
In the comments to the problem it was also suggested to find the minimum percentage of supporters, at which MM can win.
This number is accurate. I'll write the solution in the evening, let people think about it. Maybe someone can do even less?
;)
Another one, but my own solution seems too simple to me:
(4) Find the smallest number from the set of all those natural numbers which cannot be defined by less than sixteen words.
Just scored. The "too simple" solution turned out to be correct! But the problem is undoubtedly "bad".
Another one:
(4) Megabrain is imprisoned and told that he can only get out of here if he can open the doors. The doors are opened with the following device: there is a "parallelepiped" in front of the entrance, in which holes are made on the sides on four sides. There is a lever in each hole. The levers do not stick out of the holes, but are hidden in recesses, i.e. the position of the levers is not visible. The levers can go up and down. The doors open when all four levers are either up or down. Megamind can put his hand or both hands into the recesses and then manipulate the levers (raise, lower, do not change position). Then he has to take his hands out of the recesses. As soon as the hands are taken out, the parallelepiped automatically unfolds and once it stops it is impossible to tell where the hands have been put. Water pours into the prison, it floods the cell in 10 minutes, the parallelepiped rotates for exactly one minute. How does Megamozg escape?
More:
(5) Megamozg chases the dastardly criminal Occupier, who tries to hide in the basement of his house. The basement is 3 narrow straight corridors of equal length, diverging propeller-like from a small room and ending in a dead end. The basement is dark and Megamozg can only discern the culprit from a distance of no more than 10 metres. Megamuzg's speed is twice the speed of the Occupant. At what maximum corridor length can the Megamogg be guaranteed to catch the criminal (no proof of optimality required)?
A comment from the presumptive solver:
In order to eliminate unnecessary questions at the initial stage, which probably will occur to each of you in a discussion with the moderators, I want to make my visions:
1. There are no entrances-exits to the basement. Consider that MM and the Occupant materialized/teleported there, or first the occupant climbed in through the hatch, then MM, locking the hatch with his lock
2. Initially MM does not see the Occupier, and the range of vision of the Occupier is much greater than that of MM.
3. The corridors are so narrow that from a distance of 10m, the MM cannot determine the direction of movement of the Occupier leaping through a miserably small "room" from one corridor to another.
4. The angle between any two adjacent corridors can be assumed to be 120 deg. and, the same magnitude is equal to the angle of view of the instantaneous focus of the MM.
5. The maximum speed of the MM is not more than twice the maximum speed of the Occupant.
6. MM, of course, can turn around and can even run backwards, but there is a good chance of getting hit in the "pumpkin" by the Occupier, and the pursuit is over :)
7. The first answer to this task is likely to be wrong.
Good luck!
A comment by the presumptive decider: