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Lucky seven (Posted on 2010-02-05) Difficulty: 4 of 5
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.)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Hints/TipsMy solution- errataAdy TZIDON2010-03-12 01:37:35
SolutionsolutionTheKPAXian2010-02-10 11:30:38
re: Such a number exists. -- program for verification onlyCharlie2010-02-05 16:47:53
Such a number exists.Jer2010-02-05 16:30:09
SolutionsolutionJustin2010-02-05 14:02:04
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