November 23 is celebrated as Fibonacci Day. Because 1123... is the beginning of the Fibonacci sequence
The nth Fibonacci number is the sum of the previous two Fibonacci numbers, starting with 1,1.
F(n) = F(n-1) + F(n-2)
Hence we get 1, 1, 2, 3, 5, 8, 13, 21, …
The Fibonacci sequence (and the golden ratio phi φ which is related to Fibonacci numbers) can be found in nature, works of art, architecture, music and even stock market analysis.
The Fibonacci sequence first appeared in the western world in the book Liber Abaci (The Book of Calculation, 1202) by Italian mathematician Fibonacci, where it is used to calculate the growth of rabbit populations.
The Fibonacci sequence appears in Indian mathematics, going back as early as c. 450 BC–200 BC.
Fibonacci (~1170 - 1240–50), also known as Leonardo Bonacci, was an Italian mathematician, from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages."
In his book Liber Abaci (1202), Fibonacci introduced the Hindu–Arabic numeral system, with 10 digits including a zero and positional notation, to Europe. It had a profound impact on European thought as it replaced the use of Roman numerals. en.wikipedia.org/...
Johannes Kepler observed that the ratio of consecutive Fibonacci numbers converges to the Golden Ratio φ. www.goldennumber.net/...
I.e., F(n) / F(n-1) -> φ, as n -> infinity.
φ = 0.5 + sqrt(5)/2 = 1.618033988749894...
F(n) can also be computed using Binet's formula -
F(n) = (φ^n - (-φ)^-n) / sqrt(5)
The Golden Ratio, aka The Divine Proportion, has been studied by mathematicians since ancient Greece and has been used extensively in art and architecture.
Now, let’s solve today’s puzzle composed in 1875 by noted American chess composer William Meredith (1835-1903). 100 of his puzzles are featured in the book “100 Chess Problems”, each with commentary by a different problemist.
P.S.
The chess puzzle is published on Sundays, Tuesdays and Thursdays at 6:00 p.m. ET.
It is customary for advanced players to wait till midnight ET before posting the full solution. Before then, they provide some stats about the solution (e.g., the minimum number of distinct checkmate moves), help guide others, and sometimes post hints. But there are no hard-and-fast rules; feel free to post comments as you please.
Online Board
Solution (shows first move only)
Full Solution
