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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)
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:
Therefore d=3 and c=2
and the quotient's last figures are 6823.
Please see Justin's solution(simple and beautiful) and Jer's and Charlie's verifications.)
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