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Chain Reaction (Posted on 2007-04-01) Difficulty: 4 of 5
In a competition, cyber-dominoes were featured.

Nine (9) small maps, each being a 7 x 7 grid [as below] are provided. Each shows domino positions and the direction of fall.

When these small maps are arranged as a 3 x 3 grid, this large map fits a grid [21 x 21] from A to U horizontally and 1 to 21 vertically. Each map needs to be rotated 90°, 180°, or 270° clockwise and piece “E” shouldn't be rotated 180°.

Tasks:
1. When these are rearranged as a 3 x 3 grid, the reconstructed figure should form something that has two mathematical interpretations.

2.A minimum of extra dominoes need to be added to ensure that ALL will fall.

Domino Rules:
1. A domino will only topple if its fall is 135° or 180° to that of its striker; ie, its cell shares an edge or vertex with the striker, as in the actions shown below the main graphic.
2. The first domino falls from the "X" within Map A, and in the direction of the arrow in the white cell.

Note:
1. Such a layout will not work using discrete objects in the physical world, thus the cyber/computer inference.
2. My 3 x 3 solution grid is, eg: " C2, G1, D3,.........." where the numeral represents the 90° clockwise rotations.
3. My reader might care to view "Box it up" which bears a similarity but is not an exact replication of this task.

  Submitted by brianjn    
Rating: 4.5000 (2 votes)
Solution: (Hide)
While what was to have been my original solution let me give credit where credit is due.
The solution which I erroneously considered to be unique is follows. Acknowledgments will be found after.
*************************************************
*************************************************
In the problem text I defined 90 degree clockwise rotations as unit increments. The input grid for the first task is therefore:
C1  A2  G3

D1  I2  H1

E3  F1  B2

Added dominoes
I have used compass points to indicate the direction of fall of a domino.

  J 7   E
  U10   S
  T11   SW
  S12   S
  C14   S
  P17   E

I note in compiling this solution that I carelessly gave away the last placing. Que sera. I'm not about to badger Levik to reinstitute another pic.

Significances Put together correctly, even before the added dominoes are in place, one should become aware of the tiling of "2*Pi*R" and " Pi*R^2".
*************************************************
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Acknowledgments
1. During review Jer noted that a coloured cell in Map B did not have a domino. This cell, which is P17 in the final grid should have been the background colour of the map.
2. Consider all of Dej Mar's solutions to contain P17; it was 'camouflaged'.
The first published coincides with my original.
I can't discount the D14 offering even though it upsets the aesthetic shape of the "2" by allowing C14 to be a space.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsPuzzle AnswerK Sengupta2023-12-12 06:47:47
Cyber security due diligenceCodyDunning2023-12-12 06:04:57
Cyber SecurityCodyDunning2023-09-25 06:11:58
re(3): Solutionbrianjn2007-04-04 09:35:47
re(2): SolutionJer2007-04-02 11:59:59
re: Solutionbrianjn2007-04-01 23:39:31
SolutionSolutionDej Mar2007-04-01 19:44:00
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