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Laser Reconstruction: 6 targets, 5 mirrors (Posted on 2007-12-14) Difficulty: 3 of 5
Two lasers enter a limitless space in which there are 6 targets.
One laser enters vertically downward while the other is initially horizontal from the right.

You have 5 mirrors, each of which can deflect a beam at either 45° or 135°.

Each laser beam passes through all targets only once.
Each segment of one laser beam passes exactly through 1, 2 and 3 targets
while those of the other never pass through more than two.

You may care to challenge yourself by fitting all targets into a 4 x 4 grid.
As a further challenge fit the 6 targets into a 4 x 4 grid, use the same rules but use only 4 mirrors.

Note: 1. Brian Smith's Laser Puzzle was the inspiration for this.
2. I acknowledge Brian Smith's thoughts re the use of a 4 mirror version.

  Submitted by brianjn    
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Solution: (Hide)
I expect your respective solutions will be closely
akin to the following:

          5 mirrors

            V  \Q
            * ..
            O  .
          . *  .
     B/* O*****.*****\C
       .*   *  .    *
     P\..O..O.....O  <-
          * *  . *
           */  O
            A *.
Laser "V" reflects off A onto B and then down from C having 
passed through 2, 1, 1 and 2 targets. Laser "<-" passes through 3 targets before it is reflected
via P through 2 targets to be reflected downwards
off Q through the last. _________ | |O| | | |O| | | | |O|O| |O| | | |O| | The 4 x 4 Target arrangement. 4 mirrors V \N * .. O . . * . Y/*****O*****O * . * . O * . . * * . M\.....O..O.....<- * * . */ . X _________ | | |O| | | |O| |O| |O| | | | | |O|O| | The 4 x 4 Target arrangement.

The proposal which I offered for a 4 x 4 grid using 5 mirrors, Dej Mar has used a reflection of this but used 4 mirrors.
Brian Smith has actually the same target array as what I proposed for my 4 mirror 4 x 4 grid solution except that he has a 'blank' second row and a 'blank' middle column within that grid; I have a slight sense that may have been deliberate on his part.

Brian Smith, thanks for the opportunity (collaboration and guidance) to be able to offer this.

Just before posting this, I note Brian Smith has something different again for the 4 x 4, and been quite reflective in offering a 5 mirror solution.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: 4 mirrors, 4x4 grid and 5 mirrors 4x3 gridbrianjn2007-12-26 04:32:54
Solution4 mirrors, 4x4 grid and 5 mirrors 4x3 gridBrian Smith2007-12-19 13:09:09
re(2): 4 mirrors, 5x5 grid - profession??Brian Smith2007-12-17 01:32:22
re: 4 mirrors, 5x5 grid - profession??brianjn2007-12-16 03:25:19
4 mirrors, 5x5 gridBrian Smith2007-12-16 01:58:16
Solutiona 4-mirror solutionDej Mar2007-12-15 09:39:53
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