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Two to the Three = Three to the Two? (Posted on 2005-03-22) Difficulty: 3 of 5
264   This 2x3 grid has an interesting
200   property: 264x200 = 22x60x40.

Build a similar grid using all digits from 2 to 7.

See The Solution Submitted by Old Original Oskar!    
Rating: 5.0000 (1 votes)

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Solution Further extension -- spoiler | Comment 2 of 8 |
(In reply to solution and extension--computer search--spoiler by Charlie)

If we allow repeated digits and leading zeros (but exclude those where the product itself is zero), these come up:

001     195     930     001     168     001     264     240     280     370
288     300     015     378     400     784     200     028     048     048
003     495     567     960     126     153     154     372     273     492
798     400     400     048     110     110     160     120     180     160
544     714     189     648     675     588     688     135     194     156
180     075     640     350     350     640     660     154     276     295
567     576
432     444

FOR d1 = 0 TO 9
FOR d2 = d1 TO 9
FOR d3 = d2 TO 9
FOR d4 = d3 TO 9
FOR d5 = d4 TO 9
FOR d6 = d5 TO 9
  a$ = LTRIM$(STR$(d1)) + LTRIM$(STR$(d2)) + LTRIM$(STR$(d3)) + LTRIM$(STR$(d4)) + LTRIM$(STR$(d5)) + LTRIM$(STR$(d6))
  h$ = a$
  DO
    tp = VAL(LEFT$(a$, 3))
    bt = VAL(RIGHT$(a$, 3))
    lt = VAL(MID$(a$, 1, 1) + MID$(a$, 4, 1))
    md = VAL(MID$(a$, 2, 1) + MID$(a$, 5, 1))
    rt = VAL(MID$(a$, 3, 1) + MID$(a$, 6, 1))
    IF tp * bt = lt * md * rt AND tp * bt <> 0 THEN
      col = (ct MOD 10) * 8 + 1
      row = (ct \ 10) * 3 + 4
      LOCATE row, col
      tp$ = RIGHT$("0000" + LTRIM$(STR$(tp)), 3)
      PRINT tp$;
      LOCATE row + 1, col
      bt$ = RIGHT$("0000" + LTRIM$(STR$(bt)), 3)
      PRINT bt$;
      ct = ct + 1
    END IF
    permute a$
  LOOP UNTIL a$ = h$
NEXT
NEXT
NEXT
NEXT
NEXT
NEXT


  Posted by Charlie on 2005-03-22 14:34:07
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