or u can say that that if chef mines in mine A then Chefu also mines in A not just to gain more gold but he wants that Chef get less gold so he will also work in same mine @l_returns
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But they will eventually mine and the answer canât be different that what editorial said. Why will they just shifting instead of mining when they know that they wonât get anything if they just keep shifting without mining.
Both of them knows the truth that they will not get more than what is given in editorial. They will just mine and go away. ( to focus on other business maybe XD)
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Someone really need to post this problem on math.stackexchange.
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Is rating change being delayed just because of this problem?
Yes, thatâs what Iâm trying to say.
If one miner is copying other miner because he will get less gold otherwise, the first will switch to different mine as he knows he will get more gold than what was expected from working in same mine all the time.
This will go indefinitely.
Also, after reading one comment on Codeforces, it suggests that one will try to catch other but it wonât give answer at all.
I think question should have one constraint that one should dig at least some gold to be able to switch to other mine. Then answer would be feasible.
I think the problem is more with the proof than the answer itself. There is no doubt that the answer will be the same as mentioned in the editorial. (if we donât consider the fact that they keep switching mines in infinitesimal time)
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If they play optimally, they wonât mine I think as this will go indefinitely.
Question just needs one constraint that one should dig at least some gold to be able to switch to other mine.
This isnât even a fact. This is incorrect argument. They both know the truth and they will not switch for infinite time for no reason.
When they know they arenât going to get more gold even if they switch for infinite time, why will they switch ?
This is a fictional problem.
How will both know that they have mine in finite time?
They want to play optimally and it doesnât matter to them that they are wasting time overall.
See my example above.
The one who is getting lesser gold according to my answer will try to follow the other.
The one who is getting more gold according to my answer will try to avoid the other so that he can earn more.
This will apply for all cases as different approach will give different answer and players will try to mimic the better answers. But one will just try to follow other but they wonât be able to meet in finite time.
They donât need to complete in finite time but they arenât getting anything more even if they switch for infinite time. So why not just mine and complete the game ?
Makes sense. But how to counter the argument âthey are not getting even less if they keep on doing thatâ , it is also not mentioned that game should end in finite time .
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@rananjay23 if the game doesnât end in finite time then that means that the maximality condition is not fulffiled. contradiction
Itâs just a problem. You canât expect them to think in that way.
They are trying to optimise their values.
Why would even they will start the game if one of them already knows that at the end of the game one will have less gold than what he can get.
Thatâs like glass is half full and I wonât drink unless it is fully filled when you know for sure that it will never get filled.
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How ? at any moment game has not ended so how they conclude they are getting less than what they deserve ? Like that , one might even accept to get less than optimal instead of getting nothing (due to infinite process) and the other one might get more than optimal .
You are thinking that problem has mind on their own.
Itâs also possible the one who is getting less amount may keep switching until the other agrees to give him more than optimal since itâs better to get something instead of playing infinite .If we prove this then we can say problem is correct.