All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Nine kids (Posted on 2004-09-09)
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.)

 See The Solution Submitted by e.g. Rating: 4.1250 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Brute force solutions (spoilers) | Comment 9 of 22 |

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

 Search: Search body:
Forums (0)