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 Lucky seven (Posted on 2010-02-05)
A number N consisting of a string of sevens i.e. N=77777...7777, is divisible by 199. Find the last 4 digits of the quotient. No programming, please.

 Submitted by Ady TZIDON Rating: 4.0000 (1 votes) Solution: (Hide) ANS: 6823 SOLUTION : N=199*QUOTIENT= (200-1)*QUOTIENT: Let abcd be the last 4 digits of the QUOTIENT.: Then the QUOTIENT will be terminated xy00, xy resulting from multiplying cd by 2. So the subtraction looks like: xy00 abcd ________ 7777 Therefore d=3 and c=2 x=2*d=6 y=2*C=4 and the quotient's last figures are 6823. Please see Justin's solution(simple and beautiful) and Jer's and Charlie's verifications.)

 Subject Author Date My solution- errata Ady TZIDON 2010-03-12 01:37:35 solution TheKPAXian 2010-02-10 11:30:38 re: Such a number exists. -- program for verification only Charlie 2010-02-05 16:47:53 Such a number exists. Jer 2010-02-05 16:30:09 solution Justin 2010-02-05 14:02:04

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