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+--- Thread: Riddles, brain puzzles and mathematical problems (/thread-19232.html)
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-04-2014
Prove that for any (natural) number of the form abcabc (eg 123123) is divisible with 1001 and also that the result of the division is abc.
RE: Riddles, brain puzzles and mathematical problems - Froge - 04-04-2014
(04-04-2014, 02:06 PM)BAndrew Wrote: NOTE 2: The solution is really, really short, but elegant.
q1 = kq2
q2 = kq3
...
qn-1 = kqn
substituting the above equations into each other
q1 = qn(k^(n-1))
q1/qn = k^(n-1)
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-05-2014
@Froge
Correct!
A more difficult version of this:
If
- f(3ax) / f(ax) = k
Then calculate
f(243x)/f(x)
It doesn't require any theorem or something like that. Just a basic knowledge of what a function is. The idea is the same with the previous problem (it depends on how you solved the previous riddle though).
RE: Riddles, brain puzzles and mathematical problems - Froge - 04-05-2014
more difficult? but (fun)ctions are more fun
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-05-2014
(04-05-2014, 12:19 AM)Froge Wrote: more difficult? but (fun)ctions are more fun
It is both funny and difficult. Difficult is relevant of course. It may be easy for someone.
PS. Nice pun there!
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-05-2014
You want to send a valuable object to a friend. You have a box which is more than large enough to contain the object. You have several locks with keys. The box has a locking ring which is more than large enough to have a lock attached. But your friend does not have the key to any lock that you have. How do you do it? Note that you cannot send a key in an unlocked box, since it might be copied.
NOTE: Your friend is intelligent and can understand your plan even if you can't communicate.
RE: Riddles, brain puzzles and mathematical problems - Froge - 04-05-2014
send the object
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-05-2014
(04-05-2014, 08:42 PM)Froge Wrote: send the object
Good job! You just got your valuable item stolen.
RE: Riddles, brain puzzles and mathematical problems - Froge - 04-05-2014
So it has to be sent in a box?
RE: Riddles, brain puzzles and mathematical problems - BAndrew - 04-05-2014
(04-05-2014, 09:08 PM)Froge Wrote: So it has to be sent in a box?
Yes. You have to protect it with a lock, but then your friend doesn't have the key to unlock it. How do you do it?