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

Straightforward Solution by Richard)

Richard,

Both your procedure and mine work - no doubt, but the number of operations needed is totally different .

In your case this number is proportional to the initial number and in mine- to the number of digits.

Consider a one digit number 5 . You really want to press

"add 7" (and all you have is a simple calculator) 14000 times to get 10^5- which is 5 mod7 -and then to inverse it???. Please compare it with 5==>40==> 4 ==> 60==> 6 ==>20 ==>2 ==>30==> 3 ==>10==> 1 about 25 operations!!

I agree that this consideration was not part of the question but still let us give preference to "executable" solutions.

ady

*Edited on ***February 24, 2004, 11:37 am**