perplexus.info :: Logic : Block Positions

Block Positions (Posted on 2013-08-19)

  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | C | D |  | I | H |  | E | G |  | F | B |  | E | I |  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | B | H |  | A | G |  | J | C |  | D | F |  | A | J |
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | A | E |  | B | G |  | H | J |  | H | E |  | C | B |  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | I | G |  | C | F |  | F | I |  | A | D |  | D | J |
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | G | I |  | F | D |  | B | E |  | H | J |  | H | F |  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | A | D |  | B | E |  | C | G |  | J | I |  | A | C |
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | E | F |  | I | J |  | B | A |  | C | G |  | D | E |  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | F | H |  | J | H |  | A | D |  | G | C |  | I | B |
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | J | B |  | C | D |  | F | D |  | B | A |  | H | G |  
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | C | J |  | E | A |  | H | I |  | I | E |  | G | F |
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+

Each of the 25 blocks of four letters shown above can be rotated about its center, either 90^o clockwise, 90^o anti-clockwise or 180^o. When all the blocks are in their correct orientations, all the ten rows and columns contain the letters A to J exactly once.

Sixteen of the blocks shown above are not in their correct orientations. Which 16 out of the 25 blocks have been rotated and in which direction(s)?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

BC IH EG DF JA HD AG JC FB IE IA GF HJ ED CB GE BC FI HA DJ AG DE CB IJ HF DI FB GE JH AC EF HJ AD CG BI FH JI BA GC ED JB CD IH AE FG CJ EA DF BI GH 1 4 5 6 7 9 11 12 13 14 17 18 20 23 24 25 1 1 2 1 3 3 1 3 1 2 2 3 2 2 3 2
where the next-to-last line indicates which blocks were rotated, where the numeration is in normal reading order: left-to-right within top-to-bottom, and each number on the last line indicates the number of 90^oclockwise turns are applied to the block indicated just above it.
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: bang	K Sengupta	2024-04-19 22:10:59
bang	Hedda Dunn	2024-04-19 14:13:44
computer solution	Charlie	2013-08-19 19:34:12

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