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March 17

Math problem

I'm having a hard time finding anything on this. I remember a problem similar to "if I buy an item for $5, sell it for $10, buy it back for $15, and finally sell it for $20, how much profit do I make?", but I can't find anything on it or any solutions. Any help? Therapyisgood (talk) 01:37, 17 March 2023 (UTC)[reply]

Take a sum of the amount earned and a sum of the amount paid. The net is the first minus the second. –jacobolus (t) 03:00, 17 March 2023 (UTC)[reply]

P.S. a web search for "bought sold bought sold riddle" turns up a bunch of results. –jacobolus (t) 03:23, 17 March 2023 (UTC)[reply]

You would be $5 ahead on each transaction making a total of $10. (Call it profit if you wish; but profit is defined over a long period such as a year, and takes into account all fixed costs.)

Whether the item you buy for $5 is the same as the one you buy for $15, or not, is irrelevant. Dolphin (t) 03:28, 17 March 2023 (UTC)[reply]

Alternating series ? --SilverMatsu (talk) 05:00, 17 March 2023 (UTC)[reply]

Are you looking for instances of this type of problem? Then look here. The problem is made confusing by the fact that in the two sales the same item is involved. This is not relevant, a fact also observed above by Dolphin51. Consider this version: "if I buy some item for $5 and sell it for $10, then buy some item for $15 and sell it for $20, how much profit do I make in total?" All you need to do is apply the profit formula to each of the two sales and then add the two profits to get the total. --Lambiam 08:54, 17 March 2023 (UTC)[reply]

It sounds like the kind of thing that would appear in books with titles like "1001 Math Puzzles". --RDBury (talk) 09:38, 17 March 2023 (UTC)[reply]

Prime numbers and the heat death of the universe

For large numbers with hundreds of digits or more, naively using trial division to try to prove that they are prime would ultimately lead to the heat death of the universe, because each trial division would increase the entropy of the universe, and there are so many smaller primes than the square root that it would also take an unreasonable amount of time to check them all.

So, do the known primality tests in Category:Primality tests (e.g., the Lucas–Lehmer primality test) produce less entropy than the trial division method (which is prone to the heat death of the universe)?

Of course, for very large numbers (beyond googolplex), even those primality tests would start to become inefficient and lead to the heat death of the universe, and the number itself cannot even be fully written down with all its digits. GeoffreyT2000 (talk) 14:40, 17 March 2023 (UTC)[reply]

By Landauer's principle, the heat produced by a computation itself is proportional to the number of bits that are irreversibly erased. Using reversible computing, we may keep the entropy increase at bay. Since quantum computing is inherently reversible, the damage may be contained by reducing the amount of (qu)bits involved in the wave function collapse needed to produce the final bit that answers the question. The computers we can build are somewhat limited in size by the number of atoms in the solar system, and if they get very large communication delays become the bottleneck, so prime hunting will not bring the heat death precariously much closer. --Lambiam 16:35, 17 March 2023 (UTC)[reply]