perplexus.info :: Just Math : Doubles on reverse

Doubles on reverse (Posted on 2008-09-02)

In the problem "Mirror, mirror on the wall" it was proved that no number in the decimal system doubles on reversing its digits, and answered for bases 3, 5 and 8 (base 2 has leading zero, so it´s not valid).

Generalise the answer for positive integer bases.

Submitted by pcbouhid

Rating: 3.0000 (1 votes)

Solution: (Hide)

It´s a reazonable long analytical proof. The answer is: this can only happens in numbers systems whose bases are either multiples of 3 or 2 more than a multiple of 3.

Note that 10 is not a multiple of 3 neither 2 more than a multiple of 3.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2024-04-09 11:46:50
Some patterns given (spoiler)	Dej Mar	2008-09-03 01:00:41
Analytic solution	Paul	2008-09-02 23:12:54
computer exploration -- some answers given	Charlie	2008-09-02 17:43:46

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