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 A digital arrangement (Posted on 2005-06-30)
Without using any arithmetical symbols (+, -, *, /, or similar; other math symbols; decimal comma or periods; letters; even parentheses) or, in short, anything but the digits, build a number with the digits 1, 3, 5, 7 and 9, that is equal to a number built with the digits 2, 4, 6 and 8 (each digit used once and only once).

Note: This is not a trick. It was extracted from a book edited by Angela Dunn, a mathematician who gathered problems that appeared in many scientific periodical revues!

 See The Solution Submitted by pcbouhid Rating: 3.2857 (7 votes)

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 re: A solution and question | Comment 2 of 20 |
(In reply to A solution and question by owl)

`1579 3        26 481957 3        682 45179 3        26 847915 3        426 89157 3        42 689175 3        426 89715 3        842 6`

from

DECLARE FUNCTION conv! (s\$, b!)
DECLARE SUB permute (a\$)
CLS
a\$ = "13579"
b\$ = "2468"
FOR i = 1 TO 120
FOR bd1 = 1 TO 3
n1\$ = LEFT\$(a\$, 5 - bd1): b1 = VAL(RIGHT\$(a\$, bd1))
n1 = conv(n1\$, b1)
FOR j = 1 TO 24
FOR bd2 = 1 TO 2
n2\$ = LEFT\$(b\$, 4 - bd2): b2 = VAL(RIGHT\$(b\$, bd2))
n2 = conv(n2\$, b2)
IF n1 = n2 THEN
PRINT n1\$; b1, n2\$; b2
END IF
NEXT
permute b\$
NEXT
NEXT
permute a\$
NEXT

FUNCTION conv (s\$, b)
t = 0
FOR i = 1 TO LEN(s\$)
t = t * b + VAL(MID\$(s\$, i, 1))
NEXT
conv = t
END FUNCTION

SUB permute (a\$)
DEFINT A-Z
x\$ = ""
FOR i = LEN(a\$) TO 1 STEP -1
l\$ = x\$
x\$ = MID\$(a\$, i, 1)
IF x\$ < l\$ THEN EXIT FOR
NEXT

IF i = 0 THEN
FOR j = 1 TO LEN(a\$) \ 2
x\$ = MID\$(a\$, j, 1)
MID\$(a\$, j, 1) = MID\$(a\$, LEN(a\$) - j + 1, 1)
MID\$(a\$, LEN(a\$) - j + 1, 1) = x\$
NEXT
ELSE
FOR j = LEN(a\$) TO i + 1 STEP -1
IF MID\$(a\$, j, 1) > x\$ THEN EXIT FOR
NEXT
MID\$(a\$, i, 1) = MID\$(a\$, j, 1)
MID\$(a\$, j, 1) = x\$
FOR j = 1 TO (LEN(a\$) - i) \ 2
x\$ = MID\$(a\$, i + j, 1)
MID\$(a\$, i + j, 1) = MID\$(a\$, LEN(a\$) - j + 1, 1)
MID\$(a\$, LEN(a\$) - j + 1, 1) = x\$
NEXT
END IF
END SUB

 Posted by Charlie on 2005-06-30 20:40:36

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