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Too many threes and sixes (Posted on 2005-05-25) Difficulty: 2 of 5
The integer A consists only of 666 threes, and the integer B has only 666 sixes.

What digits appear in the product A x B ?


  Submitted by pcbouhid    
Rating: 4.0000 (5 votes)
Solution: (Hide)

Since 6 = 3 x 2, the product in question will be the same as that obtained by multiplying the integer A1 consisting of 666 digits 9, by the integer B1 composed of 666 digits 2.

A1 is 1 less than 10^666 (the digit 1 with 666 zeros).

So, when B1 is multiplied by A1, the result is the same as multiplying B1 by 10^666 (wich yields an integer composed of 666 digits 2 followed by 666 zeros), and subtracting the integer B1.

So the result is clearly 222...2221777...7778, with 665 2's and 665 7's.

So the digits that appear in the given product are 1, 2, 7 and 8.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolutionDej Mar2008-11-06 09:07:43
AnswerK Sengupta2008-11-06 05:55:44
re: A Possible Answerpcbouhid2005-05-30 16:48:22
re: A Possible AnswerSarah2005-05-30 03:03:03
A Possible AnswerSarah2005-05-30 03:00:43
SolutionNo SubjectLaura2005-05-25 20:32:43
re: Solution with proofJer2005-05-25 18:48:56
SolutionSolution with proofOld Original Oskar!2005-05-25 18:29:13
There is a pattern to itJer2005-05-25 18:09:00
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