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The Finish Line

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On November 11, 1988, Patterson called and said that the run was finished. Always careful, he proposed to verify that there was a record of each subcase before sending the results on a magnetic tape back to us. Somehow, the news of the end the plane of order 10 was spread around the combinatorics community and we were deluged with inquiries. On November 18, Patterson called again with some bad news. There was an error number 4 for one of the A2's. What is an error number 4? It had been two years since we last looked at our CRAY program. Taking out an old listing, it took us a while to determine that error number 4 was a size problem for a data structure that could not be enlarged. This A2 could not be solved with the existing CRAY program! If it had been able to handle this A2, it would have taken about 30 seconds. The only other program around that could handle this case was our slow but adaptable NPL program. After further dividing this A2 into about 200 smaller subcases, it took NPL one day to solve one of them, giving an estimate of 200 days just to solve this A2! Meanwhile, Barry Cipra from Science called and said he would like to write an article about the non-existence of a plane of order 10. What should we tell everybody? We decided that it was prudent to solve the problem first. We found that, with a small modification of the CRAY program, it could handle all but one of the subcases. So, we ran this offending subcase using NPL and bypassed the CRAY. The plane of order 10 was again dead on November 29, 1988.

There was a surprising amount of public interest in the non-existence of a finite projective plane of order 10. Besides Science, it was also reported in the New York Times and in Scientific American. One often asked question is, ``How much computer time it took on the CRAY?'' Unfortunately, we did not keep track of the computer time used on the CRAY, because we thought it was a useless figure other than demonstrating the difficulty of the problem. We were more interested in keeping statistics that might be useful for a future verification by someone else. So, we had to make an educated guess and said 3,000 hours. Later, Patterson suggested that it was probably closer to 2,000 hours. So, our CRAY program was proceeding nodes at a rate of about nodes per second.

After the burst of publicity, we finally managed to read the magnetic tape containing the statistics. To our horror, we found another A2 with an error number 4. However, we knew exactly what to do this time and there was no panic. It was handled exactly the same way as the previous one. By the end of January 1989, the plane of order 10 was dead a third and hopefully the final time.


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