[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 295

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Mathemat, not decided. I give up.

 
Well, let Mischek tell you, he knows best. Hint: the stick is not to be transferred from a number.
P.S. In medieval times, before the Arabic number system came to Europe, only mathematicians of a very high level were able to calculate numbers in the Roman number system. So don't get too upset :)
 
Mathemat писал(а) >>
Let Mischek tell you, he knows best. Hint: you don't have to move the stick from the number.
From "equal" make it "not equal". I've already thought about it, but it's not interesting, there must be something else.
 
Mathemat >>:
Ну пусть тады Mischek скажет, ему-то точно виднее. Подсказка: палочку надо перенести не из цифры.
P.S. В средние века, до того как в Европу пришла арабская система счисления, искусством вычислений с числами в римской системе счисления владели только математики весьма высокого уровня. Так что не расстраивайся особо :)


Man, I thought you and Rich were talking about something else.
From the plus stick to the left, you get VII - IV = III.
Rich, stop kidding around.)
I don't believe it.
 
Mischek писал(а) >>


Man, I thought you and Rich were talking about something else.
From the plus stick to the left, you get VII - IV = III.
Rich, stop kidding around.)
>> I don't believe it.


Geez, Mischek, but the lengths are different :)))

 
Richie >>:


Ё-маё, Mischek, но длины палок то разные :)))


Everything Sergei
You're grounded.
Holiday without a computer or TV
Tell your teacher tomorrow about the length of the stick
Go to sleep
 
Mathemat >>:
Ну что, MetaDriver, выкладываем решение этой задачки или нет? А я пока поищу еще что-нибудь завлекательное - комбинаторное или геометрическое.

Yep.

 
Mischek >>:
Всё Серёга
Ты Наказан
Каникулы без компа и телевизора
Про длину палки завтра училке поведай
иди спать

:))

Harsh.

 
I remind you of the problem:
На доске нарисовано поле для игры «в цифры»: (((((((((_?_)?_)?_)?_)?_)?_)?_)?_)?_) . Двое играющих ходят по очереди. Первый игрок начальным ходом записывает на месте первого (самого левого) пробела (_) какую-нибудь цифру. Каждый дальнейший ход состоит в том, чтобы записать цифру на месте очередного пробела и заменить стоящий слева вопросительный знак(?) на знак сложения или умножения. При этом ни одна цифра не должна встретиться дважды. В конце игры вычисляют значение полученного выражения. Если это число чётное, то выигрывает первый игрок, нечётное — второй. Кто выигрывает при правильной игре?
And here is the solution, which I wrote in a private message.
Note that if the last digit is left and it is even, the second player cannot win if the result before was even.
If the last one is odd, the second player will always win (either multiply the previous odd total by the last one, or add the last one to the even total). So part of the first one's strategy is to make the odd ones run out quicker. He may have to pick them all with the optimal strategy of both.
In short, the optimal strategy of the first is to start with the odd one and bet them all the time. The optimal strategy of the second one is not to bet the odd ones.
If the second makes a mistake and bids an odd one in turn, the odd ones will run out before the last move (a move is a step for each side), and only the even ones will remain. Then the first will definitely win by betting an even with multiplication.
Probably before the last move the signs can be any.
(( (((((((N ?H)?N)?N)?N )?
Now the first one's move depends on the intermediate result. He has to put the last remaining H, but which sign? If the achieved result is even, he must multiply and win. If the result is odd, he must add.
In short, the first always wins.
 
The numbers from 1 to 2002 are written out in a row. Two players play, taking turns. It is allowed to cross out any of the numbers along with all their divisors. The one who crosses out the last number wins. Prove that the first player has a way to play so that he always wins.

Environmentalists protested against the large volume of logging. The chairman of the timber company reassured them as follows: "There are 99 per cent pine trees in the forest. Only pines will be felled, and the percentage of pines will remain almost unchanged after felling - 98 percent of pines. What part of the forest will be felled?

Monsters, please: don't post the solution to the second problem yet, eh?
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