[seqfan] Re: To walk on a grid

[Eric Angelini]

Yes Allan, your last interpretation
is the correct one -- my apologizes
for making easy things complicated
:-((

Catapulté de mon aPhone

> Le 31 août 2015 à 19:32, Allan Wechsler <acwacw at gmail.com> a écrit :
> 
> I am having trouble following the explanation. Do the arrows belong to the
> individual squares, or do I carry the arrow with me? At first, I thought
> that each square has its own arrow, which is left behind in its home square
> when I walk away. But if that were true, then 1111 would not take me home,
> because each new square I encounter would have an arrow pointing North,
> which had never been altered.
> 
> I think, from the rest of your explanation, that there is really only one
> arrow, showing the current direction I am facing. That is consistent with
> the rest of the data you give. Is this interpretation correct?
> 
> On Mon, Aug 31, 2015 at 11:10 AM, Eric Angelini <Eric.Angelini at kntv.be>
> wrote:
> 
>> 
>> Hello SeqFans,
>> Let's imagine an infinite grid of side-1 squares covering the plane.
>> On the floor of each square there is an arrow pointing to the North.
>> If I drop an integer N (say 27) on one of the squares, this is what
>> will happen :
>> (1) I will read the leftmost unread digit « d » of N (here, 2) and
>>    turn the arrow to the right if « d » is even (this is the case
>>    here with 2), else to the left (if « d » is odd);
>> (2) I will move « d » squares in the new direction (here, 2 squares
>>    to the East);
>> (3) I will go back to instruction (1) as long as there are unread
>>    digits in N.
>> 
>> Question:
>> For what N's does one go back to the starting square?
>> 
>> The integer 1111 is such an N, of course.
>> As are 2222, 3333, etc.
>> As is 1213311
>>   or 1215331
>>   or 1217351
>>   or 1219371.
>> As is 202 - but this is tricky! -- Explanation for N = 202:
>> 1) Turn the arrow of the origin square to the right (East) - as
>>   the leftmost « 2 » is even;
>> 2) Walk 2 squares in this direction;
>> 3) Turn the arrow of the square to the right (South) - as « 0 »
>>   is even;
>> 4) Walk 0 square in this direction;
>> 5) Turn the arrow of the (same!) square to the right (West) - as
>>   the rightmost « 2 » is even;
>> 6) Walk 2 squares in this direction: you're back on the origin
>>   square.
>> 
>> Best,
>> É.
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> 
>> _______________________________________________
>> 
>> Seqfan Mailing list - http://list.seqfan.eu/
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/