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 Too many threes and sixes (Posted on 2005-05-25)
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 ?

JUST PENCIL AND PAPER !!!

 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.

 Subject Author Date Solution Dej Mar 2008-11-06 09:07:43 Answer K Sengupta 2008-11-06 05:55:44 re: A Possible Answer pcbouhid 2005-05-30 16:48:22 re: A Possible Answer Sarah 2005-05-30 03:03:03 A Possible Answer Sarah 2005-05-30 03:00:43 No Subject Laura 2005-05-25 20:32:43 re: Solution with proof Jer 2005-05-25 18:48:56 Solution with proof Old Original Oskar! 2005-05-25 18:29:13 PRODUCTIVE PRODUCT Ady TZIDON 2005-05-25 18:10:44 There is a pattern to it Jer 2005-05-25 18:09:00

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