[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 207
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Here's a simple task (animal lovers, and especially children, will love it):
Which floor is the best place to throw a cat?
I mean, a relative's kitten survived the 7th floor + surgery on his paw. From the 2nd floor he could have hit his head. Where did you get such an applied interest? I like maths, especially theoretical maths.
Let's go.
Find the largest number such that any first k digits of that number form a number divisible by k. That is, for example, 1236543 has this property, because 1 is divisible by 1, 12 is divisible by 2, 123 is divisible by 3, ..., 1236543 is divisible by 7. How many numbers are there in total?
если обозначить
2x+3y=a
9x+5y=b,
то, решив полученную систему относительно x и y, получим
x=(-5a+3b)/17, y=(9a+2b)/17.
Таким образом, если
I have a little even simpler.
(2x+3y) - 4*( 9x+5y) = -34x - 17u = 0(mod 17)
If one of the brackets is divisible by 17, so is the other.
However, from my solution, the number 17 comes out of the snuffbox.
1. There were five numbers written on the board. By adding each of these numbers to each one, 10 sums were obtained: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15. What numbers were written on the board?
Mathemat, areyou sure the solution exists?
Richie, it's elementary, think about it!
Here's the answer, I'll tell you the password to the archive later:)))
Mathemat, в ы уверены, что решение существует?
And I cracked the password! :-)
А я пароль взломал! :-)
mazafaka :(
Can you give us an analytical solution?
мазафака :(
аналитическое решение приведете?
It wasn't in the archive. :))
В архиве не было. :))
no keys to the flat (c) in the archive either?:))))
В архиве не было. :))
Well, I can write 10 equations with 10 unknowns. Then solve them. Boring... You can do the math in your head. ;)