Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 135
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I see the solution, yes. Iterations. I've been working on it myself, slowly.
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Let the length of the corridors be X and the occupant moves with speed V.
Then:
1) The megamorg moves at a speed of 2*V;
2) to detect an occupant, the megawatt must enter corridors at (X-10) meters.
Since the time spent by the megabrain on inspection of corridors should not be greater than the time spent by the occupant on changing the corridor, we get an inequality:
3 * (X-10) / (2*V) <= (X+10) / V
2 ilunga: Please don't tell me if you know.
I'll keep quiet because I've solved most of the problems on the site and it's unlikely you'll ask the one I haven't got credit for =)
The only thing I will say right or wrong sometimes, so people do not waste time waiting for your comments
(5) Nati on braingames.ru of the player with the nickname ilunga here.
Contender: 3 * (X-10) / (2*V) <= (X+10) / V
It turns out that 3(x-10) <= 2(x+10), i.e. x <= 50. But this is with the strategy you describe.
(5) Nati on braingames.ru of the player with the nickname ilunga here.
I have a different nickname there. You too though=)
I can write here in private (or there) if you want
P.S. well that not in real life going to look)
(4) Find the smallest number in the set of all those natural numbers which cannot be defined by less than sixteen words.
Why not make fun of them?
Look at the way the poor MMs are being mocked around here...
P.S. And your mind should be turned a little, to solve it. But it's a very easy task.
Task: Find the smallest: power (kW), capacity (l/min) and generated pressure (kg/cm^2) of the pump that provides this hang-up in the air.
The weight of the hose, the frictional energy loss of the water in the hose, the efficiency of the pump - do not take into account. Let the mass of a man with his equipment on him be 100 kg.
(4) Six megalomaniacs sit on the board of directors of a company that has made a profit of 100 shares worth $1 million each. There is a linear hierarchy among the directors: from the most senior to the most "junior". The profits are divided as follows: the chief director proposes who gets how many shares, then everyone votes, "for" or "against". If at least half of the directors vote for, they will divide the shares in the way the main director suggested. If not, the megabrain is removed from the board of directors, the next in line in the hierarchy becomes the main director and the division starts from the beginning according to the same principle. The process continues until some plan is adopted. How should the chief megabrain propose to divide the 100 shares in order to maximise profit? (All megabrains are greedy, think very logically, and no one wants to lose a seat on the board).
Comment: The task is awesome (along with that of chasing the occupier). True, it's not that complicated.
There are no numbers anymore. The whole decision comes out of the head, just include logic coupled with imagination.
The leader has to propose six ordered numbers (a vector) which unambiguously determine how much will go to whom. A rationale for its optimality is highly desirable in the decision.
The priorities are as follows: first greed, then a seat on the board of directors. And logicality is assumed by default.
The shares are indivisible, i.e. the minimum stake is 1 share (1 million quid).
The task is quite correct. It doesn't matter how it moves. What matters is the distance travelled.