Enigma 1: Serious ages
1 December 2011
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From New Scientist #1143, 22nd February 1979 [link]
“If they hadn’t invented the Closed University,” said Radiotimes of Ilea, “I shouldn’t have learned about the serious function. Every birthday now I work out how serious my new ages is. For instance, I am 27 today, and I calculate the seriousness of 27 as 4; or, as we say at the CU, S(27) = 4. That is because, as you see from the blackboard, there are 4 ways in which you can compose an arithmetical progression of one or more positive integers, in which each term is 1 greater than the previous one, with the sum of the terms totalling 27”.
“I see,” I said.
“Just to be sure you do see,” said Radiotimes, “tell me:
(a) if I live to be 100, what is/are the most serious birthday(s) I shall have had?
(b) How much over 100 should I have to live to reach a more serious birthday than that?”
This is the first Enigma puzzle ever published in New Scientist!
A £5 prize was offered for the solution (about 14.3 times the 35p cover price of the magazine).
An incomplete solution was published in New Scientist #1144, but that was followed up with a clarification in New Scientist #1145.