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