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 Two to the Three = Three to the Two? (Posted on 2005-03-22)
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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 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     370288     300     015     378     400     784     200     028     048     048`
`003     495     567     960     126     153     154     372     273     492798     400     400     048     110     110     160     120     180     160`
`544     714     189     648     675     588     688     135     194     156180     075     640     350     350     640     660     154     276     295`
`567     576432     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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