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
Not the most rigorous proof, but.... by Penny)
P,
..." Now convert 7 to 1.
7 -- > 14 --> 41 --> 48 --> 1000 (1000=48+[7*136]) --> 1"..
or - shorter- :
7 -- > 14 --> 21 --> 28--> 35 --> 53 --> 60--> 6--> 13--> 20 -->2 -->9 -->16 -->23 -->30-->3 -->10 -->1
AND;
....."LOOP:
N=N+7
If a power of 10, less N, is a multiple of 7, add that multiple to N, reverse the digits to convert N to 1, exit.
Reverse the digits of N.
Repeat the above test...."
RE: " Reverse the digits of N." N was defined as an 1-digit number.
ady
remarks: Not the most rigorous proof, but....
