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 112233....99 scrambled (Posted on 2015-05-13)
Show that there is only one number which concatenated with its sixth power creates an 18 digit number with all non-zero digits occurring exactly twice.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 Always in the last place you look - spoiler | Comment 1 of 2
It is easy to figure the number sought must be from 215 to 316 which is only 101 numbers to check (actually even fewer since it can't contain zero.)

My calculator only displays 8 true digits in table mode but this was enough to eliminate all but 12 possibilities (most of the sixth powers could be seen to contain a zero, but some have 3 of a digit.)

Using a bigger calculator to check these 12 leaves us with only one number - the last one on the list = 314

314^6=958468597212736

It's pretty amazing this number exists at all.  I wonder if there are any such numbers with other powers.

 Posted by Jer on 2015-05-13 12:14:49

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