vol of number of total volume
each cube cubes
red 125 (NIL) 1610 (NONE) 201250
blue 64 (NO^(3/2) = OZ) 21413 1370432 *
yellow 4096 (ZERO) 16 (NO) 65536
-------
1637218 (NOTHING)
The *'ed line contains the answer: 21,413 blue cubes.
DEFDBL A-Z
CLS
PRINT "In order: red, blue, yellow."
FOR n = 1 TO 9
taken(n) = 1
FOR i = 0 TO 9
IF taken(i) = 0 THEN
taken(i) = 1
FOR l = 0 TO 9
IF taken(l) = 0 THEN
taken(l) = 1
nil = n * 100 + i * 10 + l
cr = INT(nil ^ (1 / 3) + .5)
IF cr * cr * cr = nil THEN
FOR o = 0 TO 9
IF taken(o) = 0 THEN
taken(o) = 1
no = 10 * n + o
sr = INT(SQR(no) + .5)
IF sr * sr = no THEN
FOR z = 1 TO 9
IF taken(z) = 0 THEN
taken(z) = 1
FOR e = 0 TO 9
IF taken(e) = 0 THEN
taken(e) = 1
FOR r = 0 TO 9
IF taken(r) = 0 THEN
taken(r) = 1
zero = z * 1000 + e * 100 + 10 * r + o
cr2 = INT(zero ^ (1 / 3) + .5)
IF cr2 * cr2 * cr2 = zero THEN
FOR t = 0 TO 9
IF taken(t) = 0 THEN
taken(t) = 1
FOR h = 0 TO 9
IF taken(h) = 0 THEN
taken(h) = 1
FOR g = 0 TO 9
IF taken(g) = 0 THEN
taken(g) = 1
nothing = n * 1000010 + o * 100000 + t * 10000 + h * 1000 + i * 100 + g
none = no * 100 + n * 10 + e
volRed = nil
volBlue = sr * sr * sr
volYellow = zero
remVol = nothing - no * volRed - none * volBlue
q = INT(remVol / volYellow)
IF q * volYellow = remVol THEN
PRINT volRed, no
PRINT volBlue, none
PRINT volYellow, q, "*"
END IF
remVol = nothing - no * volBlue - none * volRed
q = INT(remVol / volYellow)
IF q * volYellow = remVol THEN
PRINT volRed, none
PRINT volBlue, no
PRINT volYellow, q, "*"
END IF
remVol = nothing - no * volRed - none * volYellow
q = INT(remVol / volBlue)
IF q * volBlue = remVol THEN
PRINT volRed, no
PRINT volBlue, q, "*"
PRINT volYellow, none
END IF
remVol = nothing - none * volRed - no * volYellow
q = INT(remVol / volBlue)
IF q * volBlue = remVol THEN
PRINT volRed, none
PRINT volBlue, q, "*"
PRINT volYellow, no
END IF
remVol = nothing - none * volBlue - no * volYellow
q = INT(remVol / volRed)
IF q * volRed = remVol THEN
PRINT volRed, q, "*"
PRINT volBlue, none
PRINT volYellow, no
END IF
remVol = nothing - no * volBlue - none * volYellow
q = INT(remVol / volRed)
IF q * volRed = remVol THEN
PRINT volRed, q, "*"
PRINT volBlue, no
PRINT volYellow, none
END IF
taken(g) = 0
END IF
NEXT g
taken(h) = 0
END IF
NEXT h
taken(t) = 0
END IF
NEXT t
END IF
taken(r) = 0
END IF
NEXT r
taken(e) = 0
END IF
NEXT e
taken(z) = 0
END IF
NEXT z
END IF
taken(o) = 0
END IF
NEXT o
END IF
taken(l) = 0
END IF
NEXT l
taken(i) = 0
END IF
NEXT i
taken(n) = 0
NEXT n
From Enigma No. 1462, by Albert Haddad, New Scientist, 29 September 2007
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