What is " the smallest number that can not be described in less than fourteen words " ? It is a paradox, because I just described it in thirteen words. :-)
--- Den lør 22/8/09 skrev Roger Hui <[email protected]>: > Fra: Roger Hui <[email protected]> > Emne: Re: [Jprogramming] Unforgettable times > Til: "Programming forum" <[email protected]> > Dato: lørdag 22. august 2009 17.46 > The problem is that _every_ number > has something > notable about it, so that each number is "unforgettable" > and consequently it's hard to remember any single > one of them. > > 0000 all zeros > 0001 first counting number > 0002 first prime number > 0003 first odd prime > 0004 first composite number > ... > 24 60 #: ?. */ 24 60 > 1 6 > > 0106 first number greater than 100 with 2 prime > factors > > etc. > > You have most likely heard of the story about Hardy > and Ramanujan. One day Hardy took a taxi to visit > Ramanujan. On arriving Hardy told Ramanujan that > the taxi had the 4-digit number n on its license plate, > a thoroughly unremarkable number. Ramanujan > immediately remarked that n is the first number that ... . > > I forget what n or the property was, something like, > n is the first number that can be written as the sum > of two perfect cubes in two different ways, something > typically Ramanujanish. > > Yes, that was it: > > c=: i*i*i=: >:i.200 > t=: (</~i.200) * +/~c > d=: </.~ ,t > (2=#&>d)#d > +---------+---------------+---------------+---------+-- > |1729 1729|1092728 1092728|3375001 3375001|4104 4104| ... > +---------+---------------+---------------+---------+-- > <./ {.&> (2=#&>d)#d > 1729 > I. , 1729 = t > 11 1609 > 1 + (#t) #: 11 1609 > 1 12 > 9 10 > +/ 1 12 ^ 3 > 1729 > +/ 9 10 ^ 3 > 1729 > > Now that I have worked out the number I can find the > story on the net: http://en.wikipedia.org/wiki/1729_(number) > > p.s. In my youth, when I needed to remember a (5-digit) > number for a time, I would try to compute its largest > prime factor by mental calculation. Try it and you'll > see why that works. > > > > ----- Original Message ----- > From: Kip Murray <[email protected]> > Date: Saturday, August 22, 2009 5:27 > Subject: Re: [Jprogramming] Unforgettable times > To: Programming forum <[email protected]> > > > To narrow the puzzle, > > > > times 3 4 5 NB. Unforgettable > > 1 6 2 0 > > 1 8 1 2 > > 1 2 0 7 > > timedata i. 1 8 1 2 > > 4 > > times i.8 > > 1 2 3 4 > > 1 4 1 4 > > 1 4 2 8 > > 1 6 2 0 > > 1 8 1 2 > > 1 2 0 7 > > 1 2 3 4 > > 1 4 1 4 > > > > You are encouraged to choose your own unforgettable > times seen > > on a 24-hour > > digital clock. > > > > > > Kip Murray wrote: > > > Who could forget > > > > > > times 3 4 5 > > > 1 6 2 0 > > > 1 8 1 2 > > > 1 2 0 7 > > > > > > ? > > > > > > Kip Murray wrote: > > >> Write a verb that produces unforgettable > times on a 24-hour > > digital clock: who > > >> could forget an appointment at 12:34 or 14:14 > or 14:28 > > ? It's too bad that > > >> 31:41 , 27:18 and 69:31 do not fit on the > clock. > > >> > > >> times 0 > > >> 1 2 3 4 > > >> times 0 1 > > >> 1 2 3 4 > > >> 1 4 1 4 > > >> times i. 5 > > >> 1 2 3 4 > > >> 1 4 1 4 > > >> 1 4 2 8 > > >> 1 2 3 4 > > >> 1 4 1 4 > > >> NB. Oh, well, you will do > > better than this > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ___________________________________________________________ Skal du købe ny bil? Sammenlign priser på brugte biler med Kelkoo og find et godt tilbud! - Se mere her http://dk.yahoo.com/r/pat/mmb ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
