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Block Positions (Posted on 2013-08-19) Difficulty: 3 of 5
  +---+---+  +---+---+  +---+---+  +---+---+  +---+---+ 
  | 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 90o clockwise, 90o anti-clockwise or 180o. 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)?

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1

DECLARE SUB orient (lv!)
CLEAR , , 25000
OPEN "blockpos.txt" FOR INPUT AS #1
OPEN "block positions.txt" FOR OUTPUT AS #2
OPEN "block positions selected.txt" FOR OUTPUT AS #3
DIM SHARED gr(10, 10) AS STRING, which(16), rot(16), solct, prev1, prev2
DO
    LINE INPUT #1, l$
    IF INSTR(l$, "--") = 0 THEN
        col = 0: row = row + 1
        FOR i = 1 TO LEN(l$)
            IF INSTR("ABCDEFGHIJ", MID$(l$, i, 1)) > 0 THEN
                col = col + 1
                gr(row, col) = MID$(l$, i, 1)
                PRINT gr(row, col);
            END IF
        NEXT
        PRINT
    END IF
LOOP UNTIL EOF(1)
CLOSE 1


FOR st = 1 TO 10
    which(1) = st
    orient 1
NEXT
PRINT solct
CLOSE 2: CLOSE 3

SUB orient (lv)
col = (which(lv) - 1) MOD 5 + 1
row = (which(lv) - 1) \ 5 + 1
c0 = col * 2 - 1: r0 = row * 2 - 1
FOR rota = 1 TO 4
    h$ = gr(r0, c0 + 1)
    gr(r0, c0 + 1) = gr(r0, c0)
    gr(r0, c0) = gr(r0 + 1, c0)
    gr(r0 + 1, c0) = gr(r0 + 1, c0 + 1)
    gr(r0 + 1, c0 + 1) = h$
    IF rota < 4 THEN
        good = 1
        FOR c = c0 TO c0 + 1
            FOR r = 1 TO r0 - 1
                IF gr(r, c) = gr(r0, c) OR gr(r, c) = gr(r0 + 1, c) THEN good = 0: EXIT FOR
            NEXT
            IF good = 0 THEN EXIT FOR
        NEXT
        IF good THEN
            FOR r = r0 TO r0 + 1
                FOR c = 1 TO c0 - 1
                    IF gr(r, c) = gr(r, c0) OR gr(r, c) = gr(r, c0) THEN good = 0: EXIT FOR
                NEXT
                IF good = 0 THEN EXIT FOR
            NEXT
            IF good THEN
                rot(lv) = rota
                IF lv = 16 THEN

                    FOR r = 1 TO 10
                        FOR c1 = 1 TO 9
                            FOR c2 = c1 + 1 TO 10
                                IF gr(r, c1) = gr(r, c2) THEN good = 0
                            NEXT
                        NEXT
                    NEXT
                    FOR c = 1 TO 10
                        FOR r1 = 1 TO 9
                            FOR r2 = r1 + 1 TO 10
                                IF gr(r1, c) = gr(r2, c) THEN good = 0
                            NEXT
                        NEXT
                    NEXT

                    IF good THEN
                        FOR r = 1 TO 10
                            FOR c = 1 TO 10
                                PRINT gr(r, c);
                                IF c MOD 2 = 0 THEN PRINT " ";
                            NEXT
                            PRINT
                            IF r MOD 2 = 0 THEN PRINT
                        NEXT
                        FOR i = 1 TO lv: PRINT USING "###"; which(i);: NEXT: PRINT
                        FOR i = 1 TO lv: PRINT USING "###"; rot(i);: NEXT: PRINT

                        FOR i = 1 TO lv: PRINT #2, USING "###"; which(i);: NEXT: PRINT #2, "      ";
                        FOR i = 1 TO lv: PRINT #2, USING "###"; rot(i);: NEXT: PRINT #2,

                        PRINT

                        IF which(1) <> prev1 OR which(2) <> prev2 THEN
                            prev1 = which(1): prev2 = which(2)
                            FOR r = 1 TO 10
                                FOR c = 1 TO 10
                                    PRINT #3, gr(r, c);
                                    IF c MOD 2 = 0 THEN PRINT #3, " ";
                                NEXT
                                PRINT #3,
                                IF r MOD 2 = 0 THEN PRINT #3,
                            NEXT
                            FOR i = 1 TO lv: PRINT #3, USING "###"; which(i);: NEXT: PRINT #3,
                            FOR i = 1 TO lv: PRINT #3, USING "###"; rot(i);: NEXT: PRINT #3,: PRINT #3,
                        END IF

                        solct = solct + 1
                    END IF
                ELSE
                    FOR nxt = which(lv) + 1 TO 26 - 16 + lv
                        which(lv + 1) = nxt
                        orient lv + 1
                    NEXT

                END IF
            END IF
        END IF
    END IF
NEXT
END SUB

finds


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 clockwise turns are applied to the block indicated just above it.


  Posted by Charlie on 2013-08-19 19:34:12
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