On 28/01/07, Frank Fischer <frank.fischer / s2001.tu-chemnitz.de> wrote:
> On 2007-01-28, Daniel Lucraft <dan / fluentradical.com> wrote:
> > According to my program here are the first ten integers that need two
> > '+'s:
> > ...(snip)...
> I think you're wrong. Some of those numbers don't need two '+', for
> example:
> ||||x|||||||x|||||||||||||+|||x||| = 373 (38 Toothpicks)
> ||x||||x|||||||x|||||||||||||||||||+||||| = 1069 (45 Toothpicks)
> |||x|||||x|||||||x|||||||||||+||x||||| = 1165 (43 Toothpicks)
> so my program says the first ten numbers with two '+' - but without
> warranty - are:
>
> |||x|||x|||x|||||x|||||||+|||x||||+| = 958 (43 Toothpicks)
> ||||x|||||x|||||x|||||||||||+|||x||||+| = 1113 (45 Toothpicks)
> ||||x|||||x|||||x|||||||||||+||||x||||+| = 1117 (46 Toothpicks)
> ||||x|||||x|||||x|||||||||||+|||x||||||+| = 1119 (47 Toothpicks)
> |||x||||x||||x||||x||||||+||||x||||+| = 1169 (44 Toothpicks)
> |||x|||x||||x|||||x|||||||+|||x||||+| = 1273 (44 Toothpicks)
> ||||x||||x||||x||||x|||||+|||x||||+| = 1293 (43 Toothpicks)
> |||x|||x|||x|||x||||x||||+|||x|||||||+|| = 1319 (48 Toothpicks)
> |||x|||x|||x|||||||x|||||||+|||x||||||+| = 1342 (47 Toothpicks)
> |||x|||x||||x||||||x|||||||+||||x||||+| = 1529 (46 Toothpicks)
>
> > Anyone know which the first one to need 3 is?
> Not yet :)

Well, after over 13 hours of CPU time (2GHz laptop)...

... on the 3rd revision of my code to ensure that it's only using
170Mb of memory well into the 700_000s range  (my initial version's
"|" * 700_000 is NOT the most efficient calculation at this stage and
what results is certainly not going to be of any use!)...

.... I am pleased (and relieved) to announce the first and (I think)
the lowest toothpick calculation with 3 plusses... :-)

775437: |||x||||x||||x||||x||||x||||x||||||x||||||x|||||||+||||x||||x||||x||||x|||||+|||x||||+|
 (103)

I sense some kind of exponential increase so I'm not going to even
think about trying to attempt finding 4 plusses.

-- 
Marcel