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by Brian Gladman on August 22, 2019

New Scientist Enigma 519 – Fibonacci Thimbles

by Susan Denham

From Issue #1669, 1st July 1989

One year, on my birthday I started a collection of thimbles. The following birthday l added to my collection, which went from strength to strength. In all subsequent years when I counted the thimbles on my birthday the total had increased from the previous year’s total by a number equal to the total I had on my birthday the year before that. (So, for example, my 1983 total equaled my 1982 total added to my 1981 total.) Now, by coincidence, my daughter was born on my birthday. And, with my collection growing following the described pattern, on our birthday in 1983 the number of thimbles I owned had reached exactly four times my daughter’s age on that day. On my birthday this year the total of thimbles was four times my age. On only one other occasion has the total been divisible by four, and that was in the year my son was born. How many thimbles were there in my collection on my birthday this year? How many (if any) did I have on the day my daughter was born?

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