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?
(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 20060926 23:05:17 