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C00002 00002	\|\\M1BASL30\M2NGR40L\M3NGR25\M4NGR20\M5FIX25\F2\CSTANFORD UNIVERSITY
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\|\\M1BASL30;\M2NGR40L;\M3NGR25;\M4NGR20;\M5FIX25;\F2\CSTANFORD UNIVERSITY
\F3\CSTANFORD, CALIFORNIA 94305
\F4ARTIFICIAL INTELLIGENCE LABORATORY\←L\-R\/'7;\+R\→.\→S   Telephone:
\←S\→.415-497-3330


\F1\COctober 24, 1979



Professor Allan Gottlieb
Dept. of Mathematics
York College
Jamaica, N.Y. 11451

Dear Professor Gottlieb:

\JSupplementing my letter to you dated Oct.10th, I am enclosing some additional
results relating to your problem NS16 (Palindromes) in the Aug./Sept.
Technology Review.

I rewrote my program to speed it up a bit and extended the analysis to 6-digit
numbers.  About the only significant fact that seems to emerge is that the
required number of adds seems to be going up.

It seems unlikely that any additional insight into the problem will be gained
by further calculations of this sort.

For your convenience, I am tabulating some figures taken from the two runs.\.
\F5
    Number of digits        2       3       4       5       6
    Intransigent classes    0       3      11     246     937
    Intransigent cases      0      13     233    5774       *
    Palindrome classes     18     177     331    3174    5561
    Palindrome cases       90     887    8767   84226       *
    Maximum adds for P's   24      23     21       55      64
	* not computed but total would be 900000.

\F1
\←L\→S\←R\-L\/'2;\+L\→L
Sincerely,




Arthur L. Samuel

\←S\→L
enclosure: Oct.24 results


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