[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 355

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Mathemat >>:
Млять.
MD, ну ёлы-палы, ну нельзя же так быстро!

Off to repent. ;)

// Grumpily aside: "Oh, man, there was only a limitation on knowing-beforehand!..! There was no time limit...! I have all the moves written down....!"

 
Svinozavr >>:
))) Так в "Западне Ферма" эта загадка была, если не ошибаюсь, нет?

I don't remember that one. But when watching it, I remember being very surprised by the number of matches in this thread. I was.

// By the way: it was all about speed - go, go, go, go... So I got infected. Now I can't get rid of it... ;-))

 
MD, you're forgiven :)
OK, next:
Masha and Sasha want to buy a primer. Masha is 1 penny short and Sasha is 5 pennies short. Even when they added up they were short of money. How much money does someone have and how much does a primer cost?

Another one, just for the sake of time, is very simple:
You have hired a man to chop wood. He will cut it for a week (7 days). You have a piece of gold worth 7 grams, and each day you have to pay him exactly 1 gram. But you may only chop the piece twice. How will you pay him?
 
Mathemat >>:
ОК, следующая:
Маша и Саша хотят купить букварь. У Маши не хватает 1 копейки, а у Саши - 5. Даже когда они сложились у них не хватало денег. Сколько у кого денег и сколько стоит букварь?

Masha = 4

Sasha = 0

Primer = 5

// I have no forgiveness.... !! :-(

;)

 
Yeah, MD. And let Richie solve the problem with gold :)
Here's a more serious problem:

This problem is proposed for the job interview for a "programmer" position in large companies. No special knowledge is needed to solve it, although in order to solve it accurately in the general case, information from the theory of series is needed.

There are two glass balls: red and blue. You are in a 100-storey building. You need to determine the number of the floor from which the ball will break when it falls. That is, you have to precisely specify that falling from the N-th floor the ball doesn't break, but falling from (N+1)-th floor it already breaks.

In what minimum number of steps can we be guaranteed to determine the floor in the worst case? What is the strategy of the fastest solution of the problem?

Solve the problem for the case of L storey building and m balls.

P.s.: A step is one toss of one balloon. The balloon starts to break from a certain floor.

My P.S.: In the first condition we only have two balls! I.e. after smashing the second one you have to give an unambiguous answer.
 
Mathemat >>:
Эта задача предлагается для решения при собеседовании на позицию "программиста" в крупных компаниях. Для ее решения не нужно специальных знаний, хотя чтобы точно решить задачу в общем случае необходимы сведения из теории рядов.

Есть два стеклянных шарика: красный и синий. Вы находитесь в 100-этажном доме. Вам нужно определить номер этажа, начиная с которого шарик при падении разбиваются. То есть, нужно точно указать, что при падении с N-го этажа шарик не разбивается, а при падении с (N+1)-го уже разбивается.

За какое минимальное число шагов мы можем гарантированно определить этаж в самом худшем для нас случае? Какова стратегия быстрейшего поиска решения предложенной задачи?

Решить задачу для случая L-этажного здания и m шариков.

П.с.: Шаг - это один бросок одного шарика. Шарик начинает разбиваться с определённого этажа.

A clarification is required. Do we have two types of balloons (blue and red) or two copies? I.e. if, say, a blue balloon crashes from some floor, is it dropped? Or is it replaced by its counterpart?

// Hmm. You've got an addendum in your post. And it's still confusing. Just got even more confused. Are the balls the same strength?

 
In short. If the balls are of different strengths, and presented in a single copy, you have to drop them from each floor once at a time. Starting with the first. Worst case scenario is 198 throws, assuming it's known in advance that from the 100th they'll break for sure. If this is also unknown, then 200.
 
MetaDriver >>:
Короче. Если шарики разные по прочности, и представлены в одном экземпляре, то придётся их с каждого этажа сбрасывать по разу. Начиная с первого. Итого в худшем случае 198 бросков, при условии, что заранее известно, что с сотого они разбиваются точно. Если и это неизвестно, то 200.

mumbling in the terms of the task is really annoying...

Dividing by sections with a 'golden ratio' speeds up the search.

 
They are the same in terms of durability. The colours are of the utmost importance: they cannot be repainted at all, as this is an exclusive customer whim for the encoder. There are only two balls.
P.S. The problem is really serious. I had no idea that such tasks are given as a test.
 
Only two balloons and 100 storeys? Threw the first red(blue), the second blue(red) and the exact answer?
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