bonanova Posted July 16, 2009 Report Share Posted July 16, 2009 (edited) This puzzle was originally published in 1954 in the American Mathematical Monthly, and was one of its most popular problems. The digits [not all the same] have been replaced by X's, except for the quotient where all but one have been removed! Although there are 81 x 109 possible solutions, this is really not as difficult as it looks, after some close inspection. For starters, the lone 8 is correctly placed, as the third digit of the 5-digit answer. Enjoy! . . . . . . . . . 8 . . . .---------------- X X X / X X X X X X X X . . . . . X X X . . . . . ----- . . . . . . X X X X . . . . . . . X X X . . . . . . . ----- . . . . . . . . X X X X . . . . . . . . X X X X . . . . . . . . ------- Edited July 16, 2009 by bonanova Added X to last row Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 16, 2009 Report Share Posted July 16, 2009 In the last 2 rows you have a 3 digit number cancelling a 4 digit number. Does it mean that some "leading X" can be Zero? Or was it a typo? Or is there some remainder also left?! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 16, 2009 Report Share Posted July 16, 2009 (edited) a) leading digits must be 1 (and assuming there is a remainder) b) there must be two zeroes in the quotient c) 8 times a 3 digit number is still a 3 digit number, leading number must be 1 . . . . . . . . 0 8 0 . . . .---------------- 1 X X / 1 X X X X X X X . . . . . X X X . . . . . ----- . . . . . . 1 X X X (2nd digit is 8 or 9, if digit below is 9, this is 9) . . . . . . . X X X (first digit is either 8 or 9) . . . . . . . ----- . . . . . . . . 1 X X X . . . . . . . . . X X X . . . . . . . . . ----- Edited July 16, 2009 by tbrophy Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted July 16, 2009 Author Report Share Posted July 16, 2009 In the last 2 rows you have a 3 digit number cancelling a 4 digit number. Does it mean that some "leading X" can be Zero? Or was it a typo? Or is there some remainder also left?! Ah! Thanks for pointing that out. There should of course be 4 X's in the bottom line. I've edited the OP to Make it So. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 16, 2009 Report Share Posted July 16, 2009 (edited) Aaargh!!! Twice i have tried to post the soln with details and twice i got an error and had to retype! This is the third time... Which is why this time i am only posting the solution: Quotient: 80809 Divisor: 124 Edited July 16, 2009 by DeeGee Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted July 17, 2009 Author Report Share Posted July 17, 2009 Kudos to tbrophy for the initial analysis and DeeGee who brought it home! Quote Link to comment Share on other sites More sharing options...
Question
bonanova
This puzzle was originally published in 1954 in the American Mathematical Monthly, and was one of its most popular problems.
The digits [not all the same] have been replaced by X's, except for the quotient where all but one have been removed!
Although there are 81 x 109 possible solutions, this is really not as difficult as it looks, after some close inspection.
For starters, the lone 8 is correctly placed, as the third digit of the 5-digit answer.
Enjoy!
. . . . . . . . . 8
. . . .----------------
X X X / X X X X X X X X
. . . . . X X X
. . . . . -----
. . . . . . X X X X
. . . . . . . X X X
. . . . . . . -----
. . . . . . . . X X X X
. . . . . . . . X X X X
. . . . . . . . -------
Edited by bonanovaAdded X to last row
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