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

 Antimagic square (Posted on 2011-07-12)
Let us place at random the digits from 1 to 9 into the cells of 3x3 square.
What is the probability of getting a configuration such that the 8 sums (3 rows, 3 columns and 2 main diagonals) will be represented by 8 distinct numbers?
Construct at least one such square.

Extra challenge:
Same two tasks for 4x4 square , numbers 1 to 16 and 10 distinct sums.

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 7

DEFDBL A-Z
DECLARE SUB permute (a\$)
CLS
a\$ = "123456789": h\$ = a\$
DO
a = VAL(MID\$(a\$, 1, 1))
b = VAL(MID\$(a\$, 2, 1))
c = VAL(MID\$(a\$, 3, 1))
d = VAL(MID\$(a\$, 4, 1))
e = VAL(MID\$(a\$, 5, 1))
f = VAL(MID\$(a\$, 6, 1))
g = VAL(MID\$(a\$, 7, 1))
h = VAL(MID\$(a\$, 8, 1))
i = VAL(MID\$(a\$, 9, 1))
n(1) = a + b + c
n(2) = d + e + f
n(3) = g + h + i
n(4) = a + d + g
n(5) = b + e + h
n(6) = c + f + i
n(7) = a + e + i
n(8) = g + e + c
good = 1
FOR i = 1 TO 7
FOR j = i + 1 TO 8
IF n(i) = n(j) THEN good = 0
NEXT
NEXT
IF good THEN
ctGood = ctGood + 1
END IF
ct = ct + 1
permute a\$
LOOP UNTIL a\$ = h\$
PRINT ctGood, ct, ctGood / ct, ct / ctGood

finds

` 24960         362880        6.878306878306878D-02       14.53846153846154 `

meaning 24960 of the 362880 possible ways of arranging the 9 digits had all eight totals different, for a probability of approx. 0.06878306878306878  or 1 in 14.53846153846154. The fraction reduces to 13/189.

 Posted by Charlie on 2011-07-12 16:29:00

 Search: Search body:
Forums (0)
Random Problem
Site Statistics
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox: