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 Another Divisibility Puzzle (Posted on 2006-09-25)
Determine the four smallest but different three digit positive decimal integers commencing with the same digit, such that their sum is divisible by precisely three of the said numbers.

What are the five smallest but different four digit positive decimal integers commencing with the same digit, such that their sum is divisible by precisely four of the said numbers?

 See The Solution Submitted by K Sengupta Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: General Observation -- program bug Comment 6 of 6 |
(In reply to General Observation by K Sengupta)

Indeed 3 solutions to part 2 once the "smallest" restriction is removed:

` 1020  1428  1190  1785  1717              7140 1080  1512  1260  1890  1818              7560 1140  1596  1330  1995  1919              7980 `

The bug is the failure to reinitialize tot.  The following segment of the program shows the correction in bold:

FOR d = 1 TO 9
IF digCt(d) >= 4 THEN
FOR n1 = 1 TO digCt(d) - 3
FOR n2 = n1 + 1 TO digCt(d) - 2
FOR n3 = n2 + 1 TO digCt(d) - 1
FOR n4 = n3 + 1 TO digCt(d)
upto = 0
tot = 0
FOR i = 1 TO npFct
IF fact(i) \ 1000 = d THEN
upto = upto + 1
IF upto = n1 OR upto = n2 OR upto = n3 OR upto = n4 THEN
tot = tot + fact(i)
n(upto) = fact(i)
IF upto = n4 OR tot > nbr - 999 THEN EXIT FOR
END IF
END IF
NEXT
diff = nbr - tot
IF diff \ 1000 = d THEN
IF nbr MOD diff > 0 THEN
FOR i = 1 TO 4
PRINT n(i);
NEXT
PRINT diff, nbr
END IF
END IF
NEXT
NEXT
NEXT
NEXT
END IF
NEXT

The same correction to the version of the program for part 1 fails to find additional sets of numbers satisfying the conditions.

 Posted by Charlie on 2006-09-26 23:05:17

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