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 X-ing a Division (Posted on 2009-01-12)
Solve this long division problem, where each of the x's represent a decimal digit from 0 to 9, whether same or different. None of the numbers may contain any leading zero.

x x x x x
-------------------
x x |  x x x x 0 0 0
x x
-------------------
x x x
x x
--------------------
x 0
x x
--------------------
x x 0
x x x
---------------------
x 0
x 0
----------------------

Note: Try to derive a non computer program assisted method, although computer program/spreadsheet solutions are welcome.

 See The Solution Submitted by K Sengupta No Rating

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

DEFDBL A-Z
FOR dnd = 1000000 TO 9999000 STEP 1000
FOR dvr = 10 TO 99
IF dnd MOD dvr = 0 THEN

q = (dnd \ 10000) \ dvr
r = (dnd \ 10000) MOD dvr
IF q >= 1 AND q <= 9 AND q * dvr >= 10 AND q * dvr <= 99 AND r >= 10 AND r <= 99 THEN
d = r * 10 + (dnd \ 1000) MOD 10
q = d \ dvr: r = d MOD dvr
s = q * dvr
IF s >= 10 AND s <= 99 THEN
diff = d - s
IF diff >= 1 AND diff <= 9 THEN
d = 10 * diff
q = d \ dvr: r = d MOD dvr
s = q * dvr
IF s >= 10 AND s <= 99 THEN
diff = d - s
IF diff >= 10 AND diff <= 99 THEN
d = 10 * diff
q = d \ dvr: r = d MOD dvr
s = q * dvr
IF s >= 100 AND s <= 999 THEN
diff = d - s
IF diff >= 1 AND diff <= 9 THEN
d = 10 * diff
q = d \ dvr: r = d MOD dvr
s = q * dvr
IF r = 0 THEN
PRINT dvr, dnd
END IF
END IF
END IF
END IF
END IF
END IF
END IF
END IF

END IF
NEXT
NEXT
PRINT ct

finds

16 divided into 1062000

which comes out as

`       6637516 | 1062000      96      102       96        60        48        120        112         80         80`
` `
` `

 Posted by Charlie on 2009-01-12 17:25:26

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