Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 34

 
MetaDriver:
Why the same cell? A node in any other cell can climb into the blot.

Yeah, figured that out, it doesn't change the point. There's still the requirement that there must be one blot for every hole inside a particular cell. At least somewhere.

Score.

 
Ashes:
If the grid is finite, it is enough to rotate it around one of the corners by 90 degrees.

You can go another 32.7 degrees.

But as Professor alsu found out, you can get by with shifts alone.

 
alsu:
What is wrong in my solution?))

You missed the "little" detail:Then one by one you opened seven boxes - all empty.

After opening 7 boxes - only 2 possibilities: if the letter was put somewhere first, it will be here 100%. If it was not put there - 100% it will not be there.

Probability put / not put 1/2 (by condition). I.e. after opening 7 boxes, the probabilitythat the letter is in the last box= 1/2.

 
Manov:

You left out a "small" detail:Then you opened 7 boxes one by one - all empty.

After opening 7 boxes - only 2 possibilities: if the letter was put somewhere first, it will be here 100%. If it was not put there - 100% it will not be there.

Probability put / not put 1/2 (by condition). I.e. after opening 7 boxes, probability = 1/2.

If the queue was generated by MathRand(), then alsu solution is correct = 1/9.

If only the obviously empty (with peeking) crates were opened, then 1/2.

It all depends on the interpretation of the conditions. popcorn to stock up?

 
MetaDriver: Stocking up on popcorn?
Nah, the second interpretation doesn't make sense. Unless you ask the skip.
 
TheXpert:
Nah, the second interpretation doesn't make sense. Unless you ask the cap.
I think so too.
 
Manov:

You missed the "little" detail:Then one by one you opened seven boxes - all empty.

After opening 7 boxes - only 2 possibilities: if the letter was put somewhere first, it will be here 100%. If it was not put there - 100% it will not be there.

Probability put / not put 1/2 (by condition). I.e. after opening 7 boxes, the probabilitythat the letter is in the last box= 1/2.

Initially the event "the letter is not put anywhere" is 8 times more probable than the event "the letter is placed in the 8th drawer". After that nobody moves it anywhere, hence the probability ratio remains till the end - 1 to 8, not 1 to 1.
 
MetaDriver:

It all depends on the interpretation of the conditions.

With probability 1/2 a letter is placed in one of the eight drawers of the table (chosen at random). Then 7 drawers are opened one by one - all are empty. What is the probability that the letter is in the last drawer?

Clearly described. ))) The question is also...

p.s. Read the question: what is the probability after opening 7 boxes

 
MetaDriver:

Cheat.

Yes, a bit undecided)) although it does add up.
 
Manov:

Clearly described. ))) The question is also...

Yep, time to place your bets.