The version I heard was that the math teacher wanted to have a rest, so assigned +/1+i.100 to the class. Gauss got the answer right away. The rest of the class labored for the entire hour. The only correct answer was submitted by Gauss.
On Aug 29, 2017 3:28 PM, "'Mike Day' via Programming" < [email protected]> wrote: > At the risk of getting too chatty, I'd point out that in the majority of > Project > Euler problems*, while you can (sometimes) explore the foothills of the > challenge, > including example solutions provided, with a brute-force approach, it is > generally > necessary to find ways to avoid requiring too much of either or both > memory and > compute time. > > BTW, I recall the story that Gauss answered the sum of integers problem > in his > High School class, by considering, say, the sequence 1 2 3 ... 20 21, > and its reverse, 21 20 ... 3 2 1, showing that each pair of items from > each sums > to 22, so that the sum of the two sequences is 21 * 22... No doubt > apocryhal. > > Cheers, > > Mike > > * see https://projecteuler.net > > On 29/08/2017 09:04, Skip Cave wrote: > >> There seems to be two basic approaches to this problem: >> >> 1. Generate the even numbers between 1 & 42, and add them up. >> 2. Use the formula for the sum of an arithmetic progression - e.g.: >> >> Sum=n(a+b)/2 >> *n* = number of numbers in the sequence (here 21) >> *a* = the first number in the sequence (here 2) >> >> *b* = the last number in the sequence (here 42) >> >> Generally, I like to approach these kinds of Quora sequence problems using >> a "brute force" approach, and ignore simplifying formulas. In the days >> before modern computers, formulas were developed to make computations on >> sequences like this Quora problem more tractable, particularly when the >> number of terms got large. >> >> Today, with powerful modern computers and languages, it is often easier to >> simply generate a sequence in it's entirety, and then compute some >> property >> of that sequence such as it's limit, sum, etc. to get the final result. >> This is particularly true when you have at your fingertips a powerful >> matrix language such as APL or J. >> >> For me, the obvious approach to this problem is to simply generate the >> sequence of even integers and then sum them, instead of trying to find a >> formula that relates to that specific sequence (in any case, I didn't have >> a clue where to look for such formulas). >> >> So the plan was: Generate the numbers from 0 to 42, throw out the odd >> numbers (zero doesn't matter in this problem), and then add up what's >> left: >> >> a =:i.43 >> >> +/(-.2|a)#a >> >> 462 >> >> >> My main dissatisfaction was that I was sure that this could be done in a >> single line, but I didn't know how to get the integer sequence on both >> sides of the tally/copy verb, which i wanted to use as a binary selector >> mask. >> >> Yes, thanks to Raul and others, I now realize that I could have just >> multiplied the first 21 integers by 2 to get all the even integers and >> then >> sum them, but I wanted to learn how to get the same vector of integers in >> two places in the formula without having to assign that vector to a >> variable. >> >> Raul showed me how to do that, though he used equality & multiplication to >> generate the selector mask and make the selections. >> >> +/(*0=2&|)i.43 >> >> 462 >> >> >> Raul's multiply by zero trick was cool, but my purist sensibilities still >> wanted to use selection of the even numbers as the most straightforward >> way >> to implement the sum of evens. >> >> However, Raul's approach did show me the way. I could use the copy >> operator >> to implement the selector mask, instead of multiplication >> >> +/(#0=2&|)i.43 >> >> 462 >> >> >> That worked, So we should also be able to get the sum of the odd numbers: >> >> >> +/(#2&|)i.43 >> >> 441 >> >> >> Yep. That worked too. So i should also be able use the NOT verb ".-" to >> invert the selection mask to get the sum of evens like I did in my >> original >> attempt: >> >> >> +/(#-.2&|)i.43 >> >> 43 >> >> >> AAAAK! What happened? I tried to negate the selection mask, and something >> went terribly wrong! Maybe I need to isolate the negation: >> >> >> +/(#(-.2&|))i.43 >> >> |length error >> >> | +/ (#(-.2&|))i.43 >> >> >> Nope! What am I doing wrong? How can I simply negate the selection mask, >> just like I did in my original explicit example? >> >> >> >> Skip Cave >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > > > --- > This email has been checked for viruses by Avast antivirus software. > https://www.avast.com/antivirus > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
