Easy bases

Number Theory Level 2

In which base does 25 + 31 = 100 25 + 31 = 100 ?


The answer is 6.

Sharky Kesa by Sharky Kesa , 19, United Kingdom

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3 solutions

Subham Agrawal
Mar 10, 2014

let x be the base 2x+5+3x+1=x^2 => x= 6,-1 so x=6

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Good job dude

Vinay Billa - 7 years, 2 months ago
Vishnu Bhagyanath
May 28, 2015

The sum in the digits place doesn't equal 6. This means that the digit 6 does not exist in this number system, but 5 exists. Therefore it is base 6.

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Since 5 is one of the digits, it means the base is above 5. Since the L.H.S. Is less than the R.H.S., the base is less than 10. Considering base 6, 25=2 6+5 1=17 and 31=3 6+1 1=19

Thus, 25+31= 17+19= 36 = 6^2 in base 10. In base 6, it would be 100

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