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 Shade-doku (Posted on 2007-08-02)
Every cell in the 6x6 grid is divided into four segments, each of which contains one digit. Only one of these digits is correct; the other three are red herrings! In the three starter cells (GA, LC and LE), the rogue numbers have been shaded.

Can you shade the rogue numbers in all the other cells, so that the finished grid has the numbers 1 to 6, once only, in every row, column and coloured rectangle?

 A B C D E F G 1 5 3 2 5 3 4 1 3 6 1 4 2 3 1 4 1 2 6 5 4 1 5 2 H 4 5 2 3 4 3 5 1 2 3 6 5 2 6 1 5 2 1 3 4 1 5 4 3 I 6 1 2 3 1 5 2 6 5 4 3 6 3 2 5 1 6 2 4 5 3 2 5 2 J 6 1 4 5 1 3 5 6 2 3 1 3 2 3 1 6 4 5 3 1 5 6 5 2 K 5 4 3 1 5 4 2 3 1 2 3 4 6 1 4 5 2 6 5 4 3 4 5 6 L 1 2 5 4 3 4 6 2 6 1 2 1 3 6 1 2 5 2 1 5 2 3 6 4

 See The Solution Submitted by Josie Faulkner Rating: 4.6000 (10 votes)

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 disregarding the starter squares | Comment 3 of 13 |

... there are 27 solutions.  The one that fits the starter squares is highlighted:

`123645 123645 125634 125634 132645 132645432516 432516 452316 452316 423516 423516651423 651432 631425 631452 651423 651432264351 264153 364152 364125 264351 264153516234 516324 516243 516243 516234 516324345162 345261 243561 243561 345162 345261`
` `
`135642 145632 235641 235641 325641 325641452316 523416 412356 451326 412356 451326621453 631245 651432 612435 651423 612435364125 264351 364125 364152 264135 264153516234 416523 546213 546213 536214 536214243561 352164 123564 123564 143562 143562`
` `
`325641 512634 513642 513642 523614 523614451326 423516 432516 432516 412536 431526612453 631425 621435 621453 631425 612435264135 264351 264153 264135 264351 264351536214 156243 156324 156324 156243 156243143562 345162 345261 345261 345162 345162`
` `
`531642 531642 532614 532614 541632 542631423516 423516 413526 421356 623415 213456612435 612453 621435 615432 135246 631542264153 264135 264351 364125 264351 164325156324 156324 156243 156243 416523 456213345261 345261 345162 243561 352164 325164`
` `
`542631 543612 543612613425 621435 621453231546 135246 135246164352 264351 264531456213 416523 416325325164 352164 352164`
` `
`DECLARE SUB place (row!, col!)DATA 1235,1234,1235,1456,1346,1245DATA 2456,1235,1234,1345,1235,3456DATA 1236,1235,1256,2456,2345,2356DATA 1236,1456,1345,1356,2356,1235DATA 1456,1345,2456,2345,1234,3456DATA 1236,1245,2345,1256,1236,1246`
`CLEAR , , 9999`
`DIM SHARED b\$(6, 6), poss\$(6, 6), ct`
`CLSFOR r = 1 TO 6: FOR c = 1 TO 6  READ poss\$(r, c)NEXT: NEXT`
`place 1, 1`
`PRINT ct`
`SUB place (row, col) FOR i = 1 TO 4   c\$ = MID\$(poss\$(row, col), i, 1)   b\$(row, col) = c\$   good = 1   FOR cc = 1 TO col - 1     IF b\$(row, cc) = c\$ THEN good = 0: EXIT FOR   NEXT   IF good THEN     FOR cr = 1 TO row - 1      IF b\$(cr, col) = c\$ THEN good = 0: EXIT FOR     NEXT     IF good THEN       IF row < 4 THEN rs = 1:  ELSE rs = 4       SELECT CASE col         CASE 1, 2          cs = 1         CASE 3, 4          cs = 3         CASE 5, 6          cs = 5       END SELECT       FOR cr = rs TO row         FOR cc = cs TO cs + 1           IF cr < row OR cc < col THEN             IF b\$(cr, cc) = c\$ THEN good = 0: EXIT FOR           END IF         NEXT         IF good = 0 THEN EXIT FOR       NEXT       IF good THEN          prow = (ct  6) * 7 + 1: pcol = (ct MOD 6) * 7 + 1          IF row = 6 AND col = 6 THEN             FOR r = 1 TO 6              FOR c = 1 TO 6                LOCATE prow + r, pcol + c                PRINT b\$(r, c);              NEXT              PRINT             NEXT             PRINT             ct = ct + 1          ELSE            c = col + 1            r = row            IF c > 6 THEN c = 1: r = r + 1            place r, c          END IF       END IF     END IF   END IF NEXTEND SUB`

Edited on August 2, 2007, 11:29 am
 Posted by Charlie on 2007-08-02 11:15:49

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