Enigma 53: Calculating birthdays
2 February 2013
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From New Scientist #1196, 28th February 1980 [link]
“When where you born?” Jamie asked Camilla.
“I’ll tell you what,” she said, “I’ll write the date on your calculator as a five-figure number, made up of the date, month and last two digits of the year — for example, if it was St Valentine’s Day, 1963, I would put 14263. There we are. You see that I was born in the 1950s. How many days are there in my birthday’s month.”
“Thirty” replied Jamie confidently.
“That’s right. Now, do you see that if I were to divide the number formed by the last two digits by an odd, prime factor of the whole number the result would be a different factor of the whole number? Now I’ll multiply the whole number by that odd prime factor.”
“Why, that makes the six-figure date of my fourth birthday, and its year is 20 more than your birth-year!” exclaimed Jamie.
What was Jamie’s date of birth?
Note: As posed this puzzle seems to have no solutions. But by relaxing the condition on Camilla’s birth month having 30 days I was able to find a unique solution (which is the same as the published solution).