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 Happy 2009 to you all (Posted on 2009-02-08)
Solve this crossnumber puzzle:

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
```

D*V       = 2009 	    N + T + U   = 2009
F2 – C    = 2009 	    O – L3      = 2009
G + H     = 2009 	    P – O       = 2009
I / X     = 2009	    3Q – A      = 2009
J/2 – Z/3 = 2009           R2 – B      = 2009
K – E     = 2009 	    Y2 + 2N – W = 2009
M + S/4   = 2009```
No number begins with zero.

Note: This nice and ingenious puzzle (look at the symmetry of the grid) and some similar ones are © copyrighted but his author has granted permission for its use.
His site (with many interesting puzzles) I´ll mention in the official solution.

 See The Solution Submitted by pcbouhid No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution Comment 3 of 3 |

2009 is 7 * 7 * 41, so to factor into two 2-digit numbers, those two integers must be 49 and 41. The second digit of V is the first digit of X and so can't be a 9, as that would cause I to have six digits rather than 5 per I / X = 2009. So D=49 and V=41.

Similar constraints are applied within the program below:

DEFDBL A-Z
CLS

d = 49: v = 41
FOR f = 46 TO 54
c = f * f - 2009
FOR x = 10 TO 19
i = 2009 * x
FOR r = 55 TO 109
b = r * r - 2009
IF b MOD 10 = c \ 100 THEN
'dvfcxirb known now
FOR l = 20 TO 46
o = 2009 + l * l * l
p = o + 2009
IF (i \ 100) MOD 10 = p \ 10000 THEN
'dvfcxirblop known
q = 100 * ((o \ 1000) MOD 10) + 10 * (r \ 10) + (i \ 10) MOD 10
sBase = ((o \ 100) MOD 10) * 1000 + (r MOD 10) * 100 + (i MOD 10) * 10
FOR tFirst = 1 TO 9
s = sBase + tFirst
IF s MOD 4 = 0 THEN
m = 2009 - s / 4
IF m >= 100 AND m <= 999 THEN
IF ((m \ 10) MOD 10) = ((p \ 100) MOD 10) THEN
'dvfcxirblopqsm known
a = 3 * q - 2009
IF a >= 100 AND a <= 999 THEN
IF (a \ 10) MOD 10 = f \ 10 THEN
hBase = (a MOD 10) * 1000 + (i \ 10000) * 10
gBase = (f MOD 10) * 10
FOR g = gBase TO gBase + 9
h = 2009 - g
IF h \ 10 = hBase \ 10 + 10 * (g MOD 10) AND ((h \ 10) MOD 10) = i \ 10000 THEN
'dvfcxirblopqsmahg known; need zjnuektwy
kFirst = 9: kMid = p MOD 10
FOR nFirst = 2 TO 9
FOR nLast = 0 TO 9
n = 100 * nFirst + 10 * (l MOD 10) + nLast
jBase = 1000 * (c MOD 10) + kFirst * 100 + 10 * (l \ 10)
FOR j = jBase TO jBase + 8 STEP 2
z = (j / 2 - 2009) * 3
IF z >= 1000 AND z <= 9999 THEN
eBase = 90000 + 100 * (j MOD 10) + 10 * nLast
FOR et = 0 TO 9000 STEP 1000
FOR eLow = 0 TO 9
e = eBase + et + eLow
k = e + 2009
IF k < 100000 AND (k \ 1000) MOD 10 = n \ 100 AND (k \ 100) MOD 10 = p MOD 10 THEN
tBase = 100 * (s MOD 10) + z \ 1000
FOR t = tBase TO tBase + 90 STEP 10
u = 2009 - n - t
IF u >= 1000 AND u <= 9999 AND (u \ 10) MOD 10 = 4 THEN
IF ((u \ 100) MOD 10) = k MOD 10 THEN
yBase = 10 * (o MOD 10)
FOR y = yBase TO yBase + 9
w = y * y + 2 * n - 2009
IF w \ 100 = u MOD 10 AND ((w \ 10) MOD 10) = x MOD 10 AND w >= 100 AND w <= 999 THEN
PRINT "a ="; a
PRINT "b ="; b
PRINT "c ="; c
PRINT "d ="; d
PRINT "e ="; e
PRINT "f ="; f
PRINT "g ="; g
PRINT "h ="; h
PRINT "i ="; i
PRINT "j ="; j
PRINT "k ="; k
PRINT "l ="; l
PRINT "m ="; m
PRINT "n ="; n
PRINT "o ="; o
PRINT "p ="; p
PRINT "q ="; q
PRINT "r ="; r
PRINT "s ="; s
PRINT "t ="; t
PRINT "u ="; u
PRINT "v ="; v
PRINT "w ="; w
PRINT "x ="; x
PRINT "y ="; y
PRINT "z ="; z
ct = ct + 1
END IF
NEXT y
END IF
END IF
NEXT t
END IF
NEXT eLow
NEXT et
END IF
NEXT j
NEXT
NEXT
END IF
NEXT
END IF
END IF
END IF
END IF
END IF
NEXT
END IF
NEXT l
END IF
NEXT
NEXT x
NEXT f
PRINT ct

The result is:

`a = 241b = 1472c = 295d = 49e = 91293f = 48g = 89h = 1920i = 24108j = 5922k = 93302l = 25m = 263n = 359o = 17634p = 19643q = 750r = 59s = 6984t = 402u = 1248v = 41w = 825x = 12y = 46z = 2856`

 Posted by Charlie on 2009-02-09 01:27:53

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