Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 31
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The corners (4pc) are from three, the remaining 4pc are from four.
So the average number of cuts is 4, but I can't see less than 6 cuts :)
(3 points)
With probability 1/2 a letter was placed in one of the eight drawers of the table (chosen at random). Then 7 drawers were opened one by one - all empty. What is the probability that the letter is in the last drawer?
(5 points)
There is a circular road 100 km long on which a finite number of barrels of fuel are randomly scattered. The total amount of fuel in the barrels is 100 litres, but the distribution of fuel over the barrels is arbitrary. A car has a fuel consumption of 1 litre/km and an empty tank with a capacity of more than 100 litres. Is it possible to bypass the entire road in any direction?
Note: the car is from occupiers, like "Fuck fuel economy!
Look for the elegant solution. Elegant has no physical limitations - but there is an invariant suitable for any, including physical.
2 It is possible to drive around, but some of the barrels will probably have to be rolled up :)
Contender, all answers have to be justified. Without justification their value is zero.
Both answers are wrong: the first one is wrong as a number, the second one contradicts the condition of the problem (barrels cannot be moved).
With probability 1/2 in one of the eight drawers of the table (chosen at random) put a letter. Then 7 drawers are opened one by one - all are empty. What is the probability that the letter is in the last drawer?
Since the 7 drawers are empty, the probability is 0.5, either there is or there isn't.
The probability grew from the first box to the last box as they were opened from (1/2)/8=0.0625 to 0.5
This is exactly what a blonde would answer if asked about the chances of encountering a dinosaur :)
The probability increased from the first drawer to the last as they were opened from (1/2)/8=0.0625 to 0.5
Alas, it wasn't rising, it was falling. Something I doubt about that too. Even if it was growing, it wasn't as fast.
If the car has an empty tank, you must have a barrel of fuel next to the car just to move off. And the probability of this event is not equal to 1. So at least the first barrel will have to be rolled to the car.
Barrels are not allowed to roll! The starting point for the diversions can, however, be chosen at will.
Let's see if practicing car enthusiasts can solve this problem...