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Tenacious Divisibility Treat (Posted on 2016-04-06) Difficulty: 2 of 5
A positive integer less than 30 million is such that if we subtract 5 from it – the resulting number is divisible by 8.

At the first step, from the number (considered originally) diminished by 5 - we subtract the eighth part. We then obtain a number that also becomes divisible by 8 after 5 is subtracted from it.

At the second step, we derive another in the same way, namely by subtracting a eighth part from the number at the end of the first step diminished by 5. The resulting number is also divisible by 8 after subtracting 5.

The operation concludes at 8th step given that at the end of 7th step we get a number that is divisible by 8 after after subtracting 5.

Determine the positive integer initially before the first step.

*** The resulting number at the end of 8th step is NOT necessarily divisible by 8 after subtracting 5.

No Solution Yet Submitted by K Sengupta    
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Solution re(2): Help from a negative (solution)....WRONG | Comment 7 of 9 |
(In reply to re: Help from a negative (solution) by broll)

    G  !

 

The operation concludes at 8th step given that at the end of 7th step we get a number that is divisible by 8 after after subtracting 5.

16,777,181   DOES NOT PRODUCE SUCH NUMBER (we get 7)

The only valid numbers which do are  11,983,725  - (we get 5)

 and  28,760,941  (we get 13).

So, in the domain of non-negative numbers we have only 2 valid answers: 28,760,741  (1 after 8 steps ) & 28,760,941 (0 at the end, i.e. after 8 steps).

Dixi .

 

 

 


  Posted by Ady TZIDON on 2016-04-07 09:10:48
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