A little while ago I saw this somewhat unusual list of words:
I whiled away some time just thinking about how I would go about solving it.
That took me back a while, letting me reminisce about problem-solving techniques in general, how I learnt about them, what I found enjoyable about that learning.
For example, I still remember the first time I was presented with the “n” players in a knockout tournament, no ties, how many matches in the tournament question. n was set at 128; some people were doing the traditional 64+32+16+..+ thing, the rest of us had listened to the teacher. He very pointedly said “Think. How many losers?”. And we were ecstatic children, discovering for ourselves the truth that each match produced precisely one loser, and that the tournament needed 127 people to lose….
And so I thought to myself, of all the problems I’d seen where there was a lesson in problem-solving to be learnt, which one had I enjoyed the most?
I decided my personal winner was this one, presented to me in two parts:
(a) There is one, and only one, ten-term arithmetical progression of primes between 1 and 3000. Find it.
(b) Prove that no arithmetical progression of primes, containing eleven or more terms, can possibly exist between 1 and 20000.
I may have got the precise wording wrong, but the salient numbers are correct. See what you think. And if you have similar examples, where you learnt a simple problem-solving technique that stayed with you for the rest of your life, then please do share it.
[Incidentally, I still have no idea what Randall’s list is about. I used a progressive google search approach on the words (where you add one search term at a time and see how the top results behave) and the best I could come up with was “words at the top of successive pages in Animal Farm“. But it feels lame and unworthy. I quite liked one of the suggested answers, that the words were a sequence of captcha words. When I last looked not even Randall had figured it out.]