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        riddles >> easy >> a 101-digit number
        
(Message started by: BNC on Feb 23^rd, 2003, 11:26am)

Title: a 101-digit number
Post by BNC on Feb 23^rd, 2003, 11:26am

Consider this 101-digit number:
1. It's leftmost (MSB) digit is 6
2. Every 2 adjacent digits of the number are a 2-digit number that is divisible by either 17 or by 23.

What is the rightmost (LSB) digit?

Title: Re: a 101-digit number
Post by aero_guy on Feb 23^rd, 2003, 3:53pm

First we write out all the two-digit numbers that have 17 or 23 as a factor.

17
23
34
46
51
68
69
85
92

If we start with a six we have two possibilities,

1) 68517 terminates since there is no number on the list that starts with 7
2) 692346 repeating

[hide]So, the second set must be used, at least for the most part. It has five repeating digits, so at 100 we will just have finished the twentieth set. Since we need one last digit, the last pattern must be type 2 as well, which gives us a 6 at the end.[/hide]