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neves dda tsuj (Posted on 2004-02-22) Difficulty: 3 of 5
You have a simple (base-ten, whole number) calculator which can perform only two operations: visually reversing a number, and adding seven.

Prove that you can use this calcluator to convert any number to 1.

Notation: use ~ to denote reversal, as in
~53 = 35

No Solution Yet Submitted by DJ    
Rating: 4.5000 (6 votes)

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Solution re(2): --a slight complication IS RESOLVED | Comment 7 of 11 |
(In reply to re: my solution revisited and revised --a slight complication by TomM)

You are absolutely right by stating that some numbers do not reduce in size through my procedure.
A simple remedy will cure it.
In case where the addition of sevens causes an increase of the digits' number DO NOT INVERSE when a zero is reached but continue adding sevens till you have two zeroes as the two last digits, then INVERSE.
You can easily show that eventually it must happen- "without checking all the numbers".
Samples: 99999 (+21)===>100020(+280)===>100300===>3001 ...
78(+42)===>120(+280)===>400===> 4 ...
47(+63)===>110(+490)===>600===>6 ...
I believe the problem can be put to bed, hope you agree,

Edited on February 23, 2004, 9:27 am
  Posted by Ady TZIDON on 2004-02-23 09:18:03

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