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 Consecutive digits (Posted on 2012-08-20)
(I) What is the largest 3-digit base ten positive integer such that when multiplied by a single digit, the result is a base ten 4-digit positive integer, with consecutive digits in order (example: 1234, 4567 etc, but not 0123 or, 7968)?

(II) What is the largest 3-digit base ten positive integer such that when multiplied by a single digit, the result is a base ten 4-digit positive integer, with consecutive digits in reverse order (example: 3210, 5432 etc, but not 9786)?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 3 of 3 |

DEFDBL A-Z
CLS
FOR n = 100 TO 999
FOR mltplr = 2 TO 9
prod = n * mltplr
IF prod > 999 AND prod < 10000 THEN
p\$ = LTRIM\$(STR\$(prod))
ascend = 1
FOR i = 1 TO 3
IF VAL(MID\$(p\$, i + 1, 1)) <> VAL(MID\$(p\$, i, 1)) + 1 THEN ascend = 0
NEXT
descend = 1
FOR i = 1 TO 3
IF VAL(MID\$(p\$, i + 1, 1)) <> VAL(MID\$(p\$, i, 1)) - 1 THEN descend = 0
NEXT
good = ascend OR descend
IF good THEN
PRINT n; "*"; mltplr; "="; prod;
IF ascend THEN PRINT TAB(20); "asc.";
IF descend THEN PRINT TAB(28); "desc.";
PRINT
END IF
END IF
NEXT mltplr
NEXT

finds

` 335 * 7 = 2345    asc. 384 * 9 = 3456    asc. 432 * 8 = 3456    asc. 469 * 5 = 2345    asc. 535 * 6 = 3210            desc. 576 * 6 = 3456    asc. 617 * 2 = 1234    asc. 642 * 5 = 3210            desc. 679 * 8 = 5432            desc. 727 * 9 = 6543            desc. 776 * 7 = 5432            desc. 864 * 4 = 3456    asc. `

so the highest with a product in ascending order (I) is 864, and the highest whose product is in descending order (II) is 776.

 Posted by Charlie on 2012-08-20 12:26:50

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