## July 2007 riddle

This month's riddle follows an original suggestion by Moshe Wolf.
Prove either or both parts for your name to be mentioned as a solver. A separate list of solvers will be kept for each of the two parts.

#### Part 1:

Let n be a positive integer such that 2n-1 is a digit anagram of n (in its decimal representation). In other words, n and 2n-1 share the same digits, but in a different order. An example of such a pair would be n=37, 2n-1=73.

Show that if n's least significant digit is 3, n must also contain an 8.

#### Part 2:

Prove that for every positive integer m there exists a positive integer k, such that 2km is a digit anagram of km.

### List of solvers:

#### Part 1:

Itsik Horovitz (2 July 18:00)

#### Part 2:

Itsik Horovitz (2 July 18:00)
Or Sheffet (24 July 22:00)

Elegant solutions can be submitted to the puzzlemaster at riddlesbrand.scso.com. Names of solvers will be posted on this page. Notify if you don't want your name to be mentioned.

The solution will be published at the end of the month.

Enjoy!