[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 264

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Ну, короче, понятно, MetaDriver.
Честно говоря, не силен я в таких играх. Стратегия второго мне была известна, а первого - до сих пор нет. Но ты мне сам и помог. Тебе после моей +17 надо было -18 ставить.
Я спецом оживил игру и не знал, кто ошибется сильнее. Наверняка и у меня были ошибки.
Why not 16? Let's break it down, it's interesting.
А почему не 16? Давай разберём, интересно.
I think we take from the same pair. 1-2; 3-4 etc.
The strategy of the second, guaranteeing him a minimum of 30 modulo, is very simple:
Divide the 20 numbers into pairs (1,2), (3,4), (5,6), (7,8) ... (19,20).
As soon as the first moves (say -7), the second identifies the pair (7,8) and puts +8 (opposite sign).
This is the rule for all pairs except the last one. With the last one, the second player does the opposite, i.e. once the first player moves +20, the second player moves +19. You're not wrong here, by the way.
The worst result for the second player, if the first is not mistaken, is (modulo!): -1-1-1-...-1 (nine units) + 19 + 20 = 39 - 9 = 30. In order not to make a mistake with the optimal play of the second, the first must always take either the first or the second numbers of the pairs.
Another thing is that the first also has a strategy to prevent the second from making more than 30. I haven't figured it out yet, I can post the solution.
Mathemat писал(а) >>
Another thing is that the former also has a strategy for preventing the latter from making more than 30. I haven't figured it out yet, I can post the solution.
Go ahead.
Here (the statement is brief, well worthy of olympic status):
Mathemat, а вы что думаете, по поводу 7 сигарет? Возможно?
You see, the traditional methods have run out of steam.
I don't think anything, I'm not very good at topology at all. We've been fighting, all the attention has been grabbed.
You see, traditional methods have run out of steam.
That's my expression. Stealing :) What's your opinion on 7 cigarettes?
TheXpert, a question for you about the bugs withbugs: is the answer 10cm or not?
P.S. Uh... found the answer. Right.
Solution: move to the reference frame associated with one of the bugs. I forget the details, help me remember.