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Remainder With 3ís And 7ís (Posted on 2008-11-02) Difficulty: 2 of 5
P is a positive decimal (base 10) integer consisting entirely of the digit 3, and Q is a positive decimal integer consisting entirely of the digit 7. In the base-10 expansion of P*Q, the digit 3 is repeated precisely three times and the digit 7 is repeated precisely seven times. The product P*Q may consist of other digits besides 3 and 7.

Given that N is the minimum value of P*Q, determine the remainder when N is divided by 37.

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

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionsolutionDej Mar2008-11-03 07:13:11
Solutioncomputer solutionCharlie2008-11-02 23:43:33
P*Q, how big?brianjn2008-11-02 23:35:38
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