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1$\begingroup$ Actually the "Numbers cannot start with a 0" condition is redundant, because it would be never necessary to do so (the leading 0s can be dropped). $\endgroup$– trolley813Commented Jul 16, 2020 at 22:12
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$\begingroup$ Yes good point! I will remove that condition. $\endgroup$– Dmitry KamenetskyCommented Jul 16, 2020 at 22:55
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1$\begingroup$ Great question. I was expecting the answers to quickly hit the 10,000's+, clearly I haven't given it enough thought yet. Is there an invisible no computer tag here? Or may I answer with an algorithmic approach(assuming I can even work one out)? $\endgroup$– TCooperCommented Jul 16, 2020 at 22:57
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$\begingroup$ You can use computers if you wish - the problem is still difficult. $\endgroup$– Dmitry KamenetskyCommented Jul 17, 2020 at 2:12
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$\begingroup$ Do you collect digits one by one moving in 1 of the 8 directions? Or you somehow move in all 8 directions at the same time? $\endgroup$– klm123Commented Jul 20, 2020 at 7:47
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