Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 41
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Just now solved and confident in the solution (5 points):
A megabrain has three sticks. If they cannot form a triangle, it shortens the longest of the sticks by the sum of the lengths of the other two sticks. If the length of the sticks does not become zero and the triangle cannot be formed again, the megabrain repeats the operation, and so on. Can this process continue indefinitely?
Another one (4 points):
Megamind travelled in space and found himself on a new planet, which had only one inhabited island - just at the north pole. The inhabitants of the planet wanted to sail around the world (to swim to the South Pole and back). But unfortunately, they had only 3 ships, working on a tricky fuel called asymmetrical dimethylhydrazine, but they had plenty of this very asymmetrical dimethylhydrazine. But the tanks of each ship were only enough to sail the distance from the island to the south pole. The currents on the planet were such that if they turned off the engines, the ship would immediately drift in an unknown direction and be lost, and the depth of the sea did not allow the use of anchors. Megamozg offered them a solution, and they sailed around the world with minimum fuel consumption and with all their ships intact. What did Megamogg suggest to them? (Proof of the optimality of the solution is not required).
Gone before evening.Start at point 25. Reach the next 25, fill up (40 in the tank). Go 15 km, fill up 10 (35 in the tank). Go 30, fill up 30 (35 in the tank). Pass 30, fill up 10 (in the tank 15).Pass the remaining 15 km. The same in the opposite direction.
That's understandable. We're figuring out the size of the minimum tank here.
Start at point 25. Reach the next 25, fill up(40 in the tank). Go 15 km, fill up 10 (35 in the tank). Go 30, fill up 30 (35 in the tank). Pass 30, fill up 10 (in the tank 15).Pass the remaining 15 km. Reverse direction in the same way.
Another one (4 points):
Megamind travelled in space and came to a new planet with only one inhabited island - just at the north pole. The inhabitants of the planet wanted to sail around the world (to swim to the South Pole and back). But unfortunately, they had only 3 ships, working on a tricky fuel called asymmetrical dimethylhydrazine, but they had plenty of this very asymmetrical dimethylhydrazine. But the tanks of each ship were only enough to sail the distance from the island to the south pole. The currents on the planet were such that if they turned off the engines, the ship would immediately drift in an unknown direction and be lost, and the depth of the sea did not allow the use of anchors. Megamozg offered them a solution, and they sailed around the world with minimum fuel consumption and with all their ships intact. What did Megamogg suggest to them? (It is not necessary to prove that the solution is optimal.)
Another one (4 points):
Megamind travelled in space and came to a new planet with only one inhabited island - just at the north pole. The inhabitants of the planet wanted to sail around the world (to swim to the South Pole and back). But unfortunately, they had only 3 ships, working on a tricky fuel called asymmetrical dimethylhydrazine, but they had plenty of this very asymmetrical dimethylhydrazine. But the tanks of each ship were only enough to sail the distance from the island to the south pole. The currents on the planet were such that if they turned off the engines, the ship would immediately drift in an unknown direction and be lost, and the depth of the sea did not allow the use of anchors. Megamozg offered them a solution, and they sailed around the world with minimum fuel consumption and with all their ships intact. What did Megamogg suggest to them? (It is not necessary to prove that the solution is optimal.)
1. All three ships enter the ocean at the same time with full bulls and sail a quarter of the distance to the pole.
2. Here one of the ships keeps a quarter of a tank of fuel, pours the rest of the fuel into the tanks of the other two ships and returns to port.
3. The other two ships sail to the equator, here one of the ships keeps half a tank and gives the other the rest, then returns to port.
4. Since the last refill, the ship continuing the circumnavigation has a full tank of fuel. This is enough to sail to the pole and return back to the equator.
5...
6...
7...
The rest of the steps are symmetric to the first three, the only thing that is required is to calculate the moment of start of helping ships when they meet travelers, so that no one would have to turn off engines.
)))) but tank capacity = 30 ...
2. Here one of the ships keeps a quarter tank of fuel, pours the rest of the fuel into the tanks of the other two ships and returns to port.
Exactly 100. Example: one barrel in one place with 100 litres.
Yeah, it's beautiful.
Obviously, a cyclist can start in both directions with similar results (finding the right start). Although the starting point may be different.
The question arises: is it possible for the minimum to be different in magnitude when travelling in different directions?
The answer would shed light on the possibility of there being a "nipple", in the form of a limit on tank size (Min1 < V tank < Min2).
Two ships launch simultaneously from the north pole. At the moment they cross the equator, one of the ships takes the passengers and the rest of the fuel (exactly half, just enough to fit) from the other ship. At the moment of reaching the South Pole, the third ship sails south and meets travelers on the equator, and then all amicably return home))