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**