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Kryptos - The Cipher (Part 4) - Correctly positioned decryption of the word BERLIN

EASTNORTHEAST - This is not exactly the hint Jim Sanborn (JS) gave for K4 on the 29th of January this year. He only gave NORTHEAST - which refers to the positions 26-34 of K4's plaintext.  Beside BERLIN and CLOCK it is the third revealed plaintext word of K4. However, also this hint does not seem to help much.  However, it just so happened, that a member in the yahoo kryptos group had a conversation with Jim Sanborn due to a submitted solution. Sandborn's answer to the question contained again the last clue which surprisingly was EASTNORTHEAST at position 22-34. Jim Sanborns compass rose at CIA There is disagreement if Jim revealed this on purpose or he did it accidentially, but the new extended clue seem to be serious and valid.Interestingly, EASTNORTHEAST is exactly the direction which is illustrated on the compass rose on one of the stones around kryptos, also created by Jim Sanborn. Actually, i dont really kn...
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Using funny tricks to pass AI filters

Jailbreaking ChatGPT’s Filters: How Far Can Clever Prompting Go? Modern AI systems have sophisticated guardrails designed to block copyrighted material, harmful content, and sensitive data. But how strong are these defenses really? For years I’ve been fascinated by where these filters actually operate — on the input, during reasoning, or on the final output? This isn’t about breaking laws. It’s about understanding the limits of current alignment techniques. Can you trick the AI to output content that should actually behind some filter wall? By a happy coincidence, since i am a big fan of Quanta Magazine, i stumbled over a nice related article for a few weeks [1] which influence this post.
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MO - Puzzles (I)

❚ I  stumbled  upon a really nice MO puzzle. No, that's is not a puzzle for my dog , who is also named MO, but a puzzle taken from the well known Mathematical Olympiad, which takes places once every year. Puzzle 1: Find all triples of integers $(a,b,c) \in \mathbb{N}^3_{> 0}$ such that $$\text{I)}\;ab-c = 2^{e_1}, \;\; \text{II)}\;ac-b = 2^{e_2}, \;\; \text{III)}\; bc-a = 2^{e_3}$$ with $(e_1,e_2,e_3) \in \mathbb{N}^3$ If you have some free hours, try it for yourself. I don't think that the proof below the fold is very nice or beautiful, and also for my taste distinguished too many cases, but it is overall not that hard to follow. Proof  
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The sum of integers is -1/12 ... or not?

In the current days it seems that people picked up an old discussion and brought it to new attention in their forums. In heated debates they discuss and exchange their point of views, sometimes rather impolite than objective. They talk about infinite sums of integers, in particular divergent sums, and show how these sums can be manipulated to be equal to a finite value. This causes trouble, since it seems on the first sight rather unintuitive and wrong. The most used example for their offending object is the simple sum $$S := 1 + 2 + 3 + 4 + ... = \sum^\infty_{i=1} i$$, which can be manipulated such that it is finally equal to $-1/12$. The first one who showed this curiosity was the famous mathematician  Srinivasa Ramanujan.  And from the fact that a credible mathematician wrote down those things, there should arise some doubt that maybe perhaps there is some truth in these formulas and that the misunderstandings come from the fact, that the formulas are probably not corre...
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Brainteasers

Brainteasers are becoming increasingly popular these days. You hear them from friends, in bars and on blogs, and they are even used in job interviews to stump candidates. Some are easy, some are tricky, and some are really hard. A common teaser for example is: " A melon weights 1200gr and contains 99% water. Suppose that after one week the amount of water has reduced to 98%. What is the new weight of the melon? " Show Solution Solution: It is 600gr ! Just observe that the $1200$gr is made up of  $99\%$ water and $1\%$ melon-meat. That are $1188$gr water $12$gr melon-meat. After one week the weight of the melon reduces the $x$gr, whereof $y$gr are water and still $12$gr melon-meat. And it is known that the $y$gr water are now $98\%$, hence the $12$gr melon-meat must be $2\%$. But if $2\%$ are $12$gr, then $100\%$ are $600$gr.
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