perplexus.info :: Just Math : Not a fraction

Not a fraction (Posted on 2011-04-11)

In what base is 41/14 an integer?

P&p(or just use your head),please.

See The Solution Submitted by Ady TZIDON

Rating: 4.0000 (3 votes)

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Thinking quickly

Comment 3 of 3 |

First the base has to be at least 5, due to the presence of 4.

40/20 = 2 in all bases, but since 20>14 the integer value must be greater than 2.

44/11 = 4 in all bases but since 11<14 the integer value must be less than 4.

That means 41/14 = 3 for the fraction to be an integer.

Base 10: 14*3 = 42. Very close to 41 so I'll try adjacent bases

Base 9: 14*3 = 43. Moving away from 41, so try the other side

Base 11: 14*3 = 41. There it is. The base sought is base 11.

Posted by Brian Smith on 2016-06-29 13:42:30

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