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 Funny way to divide by seven (Posted on 2018-01-12)
"This special big number of mine allows me to get a correct answer of dividing it by 7 by simply erasing its second digit..." - declared Danny.
After a minute or two his father, W.G. quipped: "I know what digit was erased!"

Do you?

 See The Solution Submitted by Ady TZIDON No Rating

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 Analytic solution Comment 3 of 3 |
X=7Y Where X has 1 more digit than Y and both begin with the same digits means both begin with 1.  Since they both end in the same digit, they both end in 5 or 0.

Let the second digit be A and the digits after be B.
1*10^(n+1)+A*10^n+B = 7*(1*10^n+B)
3*10^n + A*10^n = 6B
(3+A)*10^n = 2*3*B
Where B<10^n

3+A must be a multiple of 3, so A=0,3,6,9

If A=0
3*10^n = 2*3*B
10^n = 2*B
B=5*10^(n-1)
Solutions look like 105, 1050, 10500 etc.

If A=3
6*10^n = 2*3*B
B=10^n
which is too large
If A>3, B just gets larger

 Posted by Jer on 2018-01-13 15:32:38

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