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neves dda tsuj (Posted on 2004-02-22) Difficulty: 3 of 5
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

No Solution Yet Submitted by DJ    
Rating: 4.5000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Hints/Tips remarks: Not the most rigorous proof, but.... | Comment 3 of 11 |
(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


  Posted by Ady TZIDON on 2004-02-22 21:51:51

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