My neighbor has nine kids (all under 21), and their ages are such that you can never pick three kids so that the middle one is the average of the ages of the extreme ones. What are their ages?

(Note that you could also say that you can never find three kids whose ages are in arithmetic progression.)

1  2  6  7  9  14  15  18  20
1  3  6  7  12  14  15  19  20

from

OPEN "ninekids.txt" FOR OUTPUT AS #2
FOR a = 1 TO 12
FOR b = a + 1 TO 13
FOR c = b + 1 TO 14
 IF c - b <> b - a THEN
  FOR d = c + 1 TO 15
  FOR e = d + 1 TO 16
  FOR f = e + 1 TO 17
  FOR g = f + 1 TO 18
  FOR h = g + 1 TO 19
  FOR i = h + 1 TO 20
   REDIM tk(21)
   tk(a) = 1
   tk(b) = 1
   tk(c) = 1
   tk(d) = 1
   tk(e) = 1
   tk(f) = 1
   tk(g) = 1
   tk(h) = 1
   tk(i) = 1
   good = 1
   FOR diff = 1 TO 11
    FOR st = 1 TO 21 - 2 * diff
      IF tk(st) + tk(st + diff) + tk(st + diff * 2) = 3 THEN good = 0: EXIT FOR
    NEXT
    IF good = 0 THEN EXIT FOR
   NEXT
   IF good THEN PRINT #2, a; b; c; d; e; f; g; h; i
  NEXT
  NEXT
  NEXT
  NEXT
  NEXT
  NEXT d
 END IF
NEXT c
NEXT b
NEXT a
CLOSE

Posted by Charlie on 2004-09-09 09:01:05