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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.
Contents
Next: Is This Really
Up:The Search for a
Previous: The Home Stretch