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
(In reply to
re: my solution revisited and revised --a slight complication by TomM)
Tom,
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,
ady
Edited on February 23, 2004, 9:27 am
re(2): --a slight complication IS RESOLVED
