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In my view you should take a lot of comfort from the fact that much of the time your inability to make your point arises, not from your failure to communicate, but from your listener's inability to hear. That was true of CajunCenturion in the Pond Prison Revisited thread, and it was true of me...

I hope I'm not embarrassing myself by giving a snap answer without thinking things through, but it seems obvious to me that if you get to pick two doors, you have a 2/3 chance of having picked the prize. Revealing an empty door doesn't change this, so the contestant should stick with his...

Looked at another way, the success rate (measured by the number of solutions divided by the number of pairs that need to be tested) declines rapidly. When the largest prime allowed is seven, 23/60 = 38.3% of the pairs tested are actually solutions. This declines to a 241/6132 = 3.9% success...

So far, so good. In exchange for a modest amount of work, we have definitively solved a bit of mathematical trivia which may be of interest to some. But of course there is nothing special about limiting the permitted prime factors to {2,3,5,7}. Adding each additional prime reveals an alarming...

Let's take a closer look at the algorithm presented in the Wikipedia article and see how much work it entails. Using the problem in this thread of finding pairs in which both numbers in the pair have no prime factors greater than seven, we need the following 15 Pell equations: x2 - 2*y2 = 1 x2...

As can be seen from my previous post, all of the valid pairs are small and easily found via computer search, or even hand calculations. If I had solved the problem this way, my greatest concern would be uncertainty whether I had searched far enough to find all of the solutions. After all...

Here are the solutions I've found. (1,2) (2,3) (3,4) (4,5) (5,6) (6,7) (7,8) (8,9) (9,10) (14,15) (15,16) (20,21) (24.25) (27,28) (35,36) (48,49) (49,50) (63,64) (80,81) (125,126) (224,225) (2400,2401) (4374,4375) Perhaps someone will independently verify these results.

In my opinion the best tribute we can pay Sid is to attempt a math challenge inspired by one of his old threads. Accordingly, I plan to work on the following problem: List all pairs of consecutive positive integers where both numbers in the pair have no prime factor greater than seven...

I would like to note the passing of Sid Hollander, who briefly posted in this Puzzles for Programmers forum under the handle SidYuca. I recently came across the following obituary: https://yucalandia.com/2022/05/30/sid-hollander-yucatans-loss-heavens-gain/ In my view Sid's contributions to...

No reasonable review process would have passed this article. Either the arithmetic is simply wrong, or there is some sort of implied approximation going on. But if the math is approximate, then the examples are not counterexamples to the Beal conjecture and the article should have been...

I hope I'm not misunderstanding your link, but counterexample 1 is [288 + 99999999999993] = 1039 The left hand side of this equation is the sum of an even number plus an odd number, hence odd. The right hand side is even, so I fail to see how equality holds. Is the author, S. Saravanan...

Interesting. Unfortunately I don't think the conjecture is amenable to the efforts of amateur mathematicians like me. My guess is that the conjecture is true, so it probably won't be productive to search for a counterexample, and attempts to prove the conjecture involve techniques that are way...

That would work, Mike, but it's not allowed in "hard mode". According to wordlegame.org The above example shows that regular mode and hard mode optimization have different optimizations with different maximum required guesses. I may never get around to programming a solution, but to me "hard...

I'm sure that anyone who plays wordle regularly has encountered words which are impossible to guess in hard mode within the allowed six guesses. I had an amusing recent experience in which a clairvoyant first guess actually hindered me finding the solution. I started with "chase", getting "h"...

I have been making Wordle a part of my morning routine since this thread was started. I have solved 15 puzzles, averaging under four guesses per word. I'm not sure how long I'll continue to solve every day - it's a moderately entertaining exercise, but there's little or no added enjoyment in...

I solved today's puzzle in five guesses without help. For the record, my progress was 1. one letter right but out of place 2. two letters right but out of place 3, two letters right and in the right place 4. three letters right and in the right place 5. solved My guess is that this game is...

Chriss, I think you're absolutely right that 979/32 is the fraction with the smallest denominator which is both in the right range to replace 30.6 in your calendar calculations and can also be expressed as a terminating fraction in binary. The options with smaller denominators are 245/8 =...

May I ask if you're experiencing any actual problems right now? Archive log files are not used at all in normal online database operations. They are only needed for doing forward recovery when restoring a database from backup. That suggests your database should be completly operational after...

@Mike Lewis I'm afraid my results using the shorter engmix.zip dictionary don't match yours. Your program doesn't seem to find a bunch of legitimate alternating consonant/vowel words that contain a 'y'. (You also seem to have manually edited out words that are minor spelling variants of...

By comparison, I get the following 21 words of 14 letters. It seems clear that your program not finding any long 'y' words is due in part to your dictionary not bothering to list words formed by adding 'ly' to a shorter word. Thus, you found 'unimaginative' but not 'unimaginatively'...