From: Frank Fischer <frank.fischer@...2001.tu-chemnitz.de>
Date: 2007-01-28T22:30:05+09:00
Subject: Re: Counting Toothpicks (#111)

On 2007-01-28, Daniel Lucraft <dan@fluentradical.com> wrote:
> According to my program here are the first ten integers that need two 
> '+'s:
> 373:   (1 + 3x4 + 3x6x4x5)   -> 38
> 958:   (1 + 3x4 + 3x3x3x5x7) -> 43
> 1069:  (1 + 3x4 + 11x4x4x6)  -> 45
> 1113:  (1 + 3x4 + 5x5x4x11)  -> 45
> 1117:  (1 + 4x4 + 5x5x4x11)  -> 46
> 1119:  (1 + 3x6 + 5x5x4x11)  -> 47
> 1165:  (1 + 3x4 + 4x6x3x4x4) -> 43
> 1169:  (1 + 4x4 + 4x6x3x4x4) -> 44
> 1273:  (1 + 3x4 + 5x7x6x6)   -> 44
> 1293:  (1 + 3x4 + 4x5x4x4x4) -> 43
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 :)

Frank