Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 146
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The shortest route is always a straight line - subject to the above
What's the big deal? Don't get too comfortable!
...
Can he do it? If so, how?
A submarine?
... If so, how murky is the water?
... in short, the brain swims from the centre to the side opposite of the goblin, visually observing that the goblin is roughly on the line boat-center-opposite shore, at a distance at which the speed of the goblin on the outer radius and the boat on a smaller radius on the water will coincide. And then the brains would jump off sharply along the shortest path to shore.
A submarine?
... if so, how murky is the water?
... the brains swim from the centre to the opposite side of the goblin, visually observing that the goblin is approximately on the line boat-center-opposite shore, at a distance at which the speed of the goblin on the outer radius and the boat on the water on a smaller radius will coincide. And then the brains would jump off sharply along the shortest path to shore.
Well, it looks like it. I'd better add some numbers, just for solidity and reassurance.
This is the text of a C program. Find three ways to change one character in it so that the program prints 20 asterisks. To change means not to add, remove, or rearrange, but to change it.
main() { int i, N=20; for (i = 0 ; i < N ; i--) { printf("*"); } }--
I found one way. :) I need two more.
This is the text of a C program. Find three ways to change one character in it so that the program prints 20 asterisks. To change means not to add, remove, or rearrange, but to change it.
--
I found one way. :) I need two more.
main() { int i, N=20; for (i = 0 ; i < N ; i--) { printf("*"); } }if you count the space as a symbol, then you've found the third one too.
P. S. MetaDriver, sent it to my personal email (let the rest of us suffer :))
if you count the space as a symbol, then you've found the third one too.
P. S. MetaDriver, sent it to my personal email (let the rest of us suffer :))
Thank you, Volodya.
The megabrain is in the boat
Yes, JJerboa suggested it correctly.
Supplement (with figures): MM's trajectory is sine (this is if goblin doesn't change running direction):
r = R/k*sin(Phi).
Here k is the ratio of the goblin's speed to MM's speed,
r is the distance from the centre of the lake,
Phi is the angle by which they turned in pursuit.
The maximum here is R/k.
Bonus: There is a boundary k0 at which MM cannot outsmart the goblin:i.e. k0 = pi + 1 ~ 4.1416.
More:
(5) Can a cube be cut into a finite number of smaller cubes so that they are all different?
Recall: (4) Six mega-brains are on the board of directors of a company which has made a profit in the form 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).