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Find number and base (Posted on 2016-03-17) Difficulty: 2 of 5

An integer n written in base b is 211 and 110
written in base b+2. Find n and b in base 10.   

No Solution Yet Submitted by Bractals    
Rating: 5.0000 (1 votes)

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Some Thoughts Off the cuff solution | Comment 2 of 6 |
Just looking at the problem I see that increasing the base by 2 cuts the lead digit in half, so I want a pair of numbers differing by 2 such that their squares are roughly in a 2 to 1 ratio.  b=5, b+2=7 comes closest with 25/49 being very close to 1/2.

Checking: 211_b5 = 56, 110_b7 = 56.  There it is: b=5 and n=56.

  Posted by Brian Smith on 2016-03-17 10:42:48
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