Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 215
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Yes. The small cube can be put on its butt altogether, so that not a single drop is inside :)
It's a shame, the cubes are too heavy, they might get crushed.)
The makers of the cubes have magically messed up and made cubes out of the substance of different magnetars (a pea weighs in the region of 100 million tons). Therefore, although their walls are very thin, they weigh seriously - well, not a billion tonnes,
;)
Although I'm willing to admit that, all other things being equal, the simplest solution is almost always preferable.
--
From the spoof that comes out when you click "more details" in this post, I like the problem:
"Prove that the sum of two consecutive prime numbers, starting with number 3, decomposes into at least three prime multipliers (possibly identical). "
The proof is simple and beautiful, although at first the problem seemed to be a "super complicated theoretical problem". :)
A problem for programmers (weight of the problem is 4):
A megabrain in a very long text needs to replace all the letters "A" with "B" and all the letters "B" with "A". The text editor allows one arbitrary set of characters to be replaced by another in the whole text. For example, replacing "AA"->"BSAA" will cause the string "AAAAAL" to become "BSAABSAAL". How does he perform the task?
FAQ (from the website):
The solution to the problem just shocked me with its unexpectedness (although I'm quite open to other solutions). I started solving it a couple of years ago, after which I disappeared from Mind Games for a year and a half. A couple of days ago I looked at it again, and about 24 hours ago sent the solution to a moderator. I have not yet received a reply, but I am 100 percent sure it is correct. The algorithm is tested on a test character set, no errors found.
1. A -> ABA
2. B -> A
3. AAA -> B
Please check on test character set.
1. A -> ABA
2. B -> A
3. AAA -> B
No, that won't work. After step 2 there will be no B characters left at all, all A characters. And after step 3 almost all the text will be replaced by B, except for one or two A characters left at the end.
P.S. Rumor has it that at least one part of the replacement expression must have at least two characters. Otherwise it will be a disaster - which is what happened to you after step 2.
1. А -> АБА
2. Б -> А
3. ААА -> Б
No, it won't. After step 2 there won't be any B characters left at all, it will be all A's. And after step 3 almost all the text will be replaced by B's, not counting one or two A's left at the end.
P.S. Rumor has it that at least one part of the replacement expression must have at least two characters. Otherwise it will be like a catastrophe - which is what happened to you after step 2.
Take away all the symbols except for A and B, it'll be easier. They're not involved in the substitution in any way. Here's a test set:
No, that won't work. After step 2 there will be no B characters left at all, all A characters. And after step 3 almost all the text will be replaced by B, not counting the one or two A characters left at the end.
P.S. Rumour has it that at least one part of the replacement expression must have at least two characters. Otherwise it will be a disaster - which is what happened to you after step 2.
If we take BA as a starting point, then
BBA
AAAA
BA
instead of AB.
P.S. 3 is not allowed)