Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 57
You are missing trading opportunities:
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
Registration
Log in
You agree to website policy and terms of use
If you do not have an account, please register
About the brick:
Throw the brick strictly from above. The ball gets caught between the brick and the plane and accelerates sharply. Theoretically, it can reach first cosmic velocity. At the desired speed and direction of motion from the plane, we sharply fire off the brick with the laser, and the ball flies away and hits the moon.
The main thing is not to hit the ball with the brick while it is still strictly on the surface of the plane.
(5)
Megamogg wants to climb to the roof of his house with a ladder. There are many ladders in the storeroom, but unfortunately, most of them are missing steps. The ladders that are missing two rungs in a row cannot be climbed by Megamogg. All of his ladders originally had N steps. All ladders have clearly defined bottom and top. How many variants of ladders could Megamogg climb?
Throw the brick strictly from above.
It wasn't strictly on top. I forgot to mention the mass - the mass of a ball is much less than that of a brick (at least 50 times less) - this is important here.
I'm organizing the picture now.
The ball bounces with a small amplitude. This is enough for the bounce to change dramatically. But the problem remains -- the maximum height to which the ball can be sent tends to 4 of the original height of the brick (the brick can increase the speed of the ball by at most 2 of its own).
I.e. for 30m you need at least 3 impacts. (i.e. + ~6 velocities of the brick).
Very clearly the problem is tested with a tennis ball and racket.
You can throw it sideways, you don't need a laser either. I mean, it's also strictly on the ball and strictly downwards, but rotated at a slight angle.
(5) Megamogg wants to climb to the roof of his house with a ladder. There are many ladders in the storeroom, but unfortunately, most of them are missing steps. The ladders that are missing two rungs in a row cannot be climbed by Megamogg. All of his ladders originally had N steps. All ladders have clearly defined bottom and top. How many variants of ladders could Megamogg climb?
There is a set of binary numbers that are N digits long. The 1st and Nth characters of these numbers are 1.
Find the number of binary numbers, in this set, provided that these numbers do not have a series of characters = 0 of length greater than 1.
Right?
Paraphrased:
...the 1st and Nth digits of these numbers are 1....
(5) All staircases have a clearly defined bottom and top
(5)
Megamogg wants to climb to the roof of his house with a ladder. There are many ladders in the storeroom, but unfortunately, most of them are missing steps. The ladders that are missing two rungs in a row cannot be climbed by Megamogg. All of his ladders originally had N steps. All ladders have clearly defined bottom and top. How many variants of stairs could Megamogg climb?
In short. We need to summarise this series:
1*2/2 + 2*3/2 + 3*4/2 + ....+(N-3)*(N-2)/2 + (N-2)*(N-1)/2 + N + 1
This will be the answer. It is desirable to make (if possible) a generalized (finite) formula for the sum of the above series.
--
Correction, not exactly that kind of series .
I'll try to correct it. My brain is a little fuzzy. :)
Where does that come from?