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Amb · Amb the Hitched.

I start with a two digit number.
I add to that number the same number that I started with, and record the second to last digit: 2
I repeat the addition, and record the second to last digit again: 3
In fact, I keep doing this and I get this sequence:

2,3,4,5,6,7,8,9,1,2,3,4,5,6,7,8,9,0,2,3,4,5,6,7,8,9,0,1,3,4,5,6,7,8,9,0,1,2,4,5,6,7,8,9,0,1,2,3,5,6,7,8,9,0,1,2,3,4,6,7,8,9,0,1,2,3,4,5,7,8,9...

Is it possible to work out what the 2 digit number is.

Is it possible to work out what any other 2 digit number is using the 2nd to last digit only as a reference. Are there impossible ones? Are there easy ones?

Suspence · Daedalian Member

If I'm understanding you right, each two-digit number can be discerned by showing the first 9 results.

Your two digit number is 10
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Suspence · Daedalian Member

I'm re-reading and perhaps I'm misunderstanding:

I start with a two digit number.
I add to that number the same number that I started with, and record the second to last digit: 2
I repeat the addition, and record the last digit again: 3

I took 10, 20 (10 + 10), 30 (30+10), etc and recorded the second to last digit each time, but it seems like the instructions go back and forth between last and second to last.
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referee · June 21st, 2004 Member

No, this one goes to 11.
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ralphmerridew · Daedalian Member

You can always determine the number with 9 results.
If the original number is not of form 10N or 10N+1, it is possible to determine the original number with 5 results.
If the original number is not of form 10N, 10N+1, 10N+8, or 10N+9, it is possible to determine the number with 4 results.

With 3 results, it's only possible if the original number is of form 10N+3, 10N+4, or 10N+7.

(Well, 3 consecutive results. Given the next-to-last digits of 2k, 3k, and 7k, it's possible to determine unless k is of form 10N or 10N+1. And given the next-to-last digits of 10k and 11k, it's trivial to determine N.)