Every whole number can be built from Fibonacci numbers in exactly one way
The Fibonacci sequence runs 1, 2, 3, 5, 8, 13, 21, 34 and on. Pick any positive whole number, say 50, and try writing it as a sum of Fibonacci numbers from that list, using each one at most once and never using two neighbors from the sequence next to each other, like 3 and 5. Can every whole number be built this way, and if so, is there ever more than one way to do it?
Reveal the answer
Every positive whole number can be written exactly one way as a sum of non-consecutive Fibonacci numbers — for 50, that's 34 + 13 + 3. Belgian mathematician Edouard Zeckendorf proved this formally in 1972, though mathematician Gerrit Lekkerkerker had already shown it two decades earlier. The result, now called Zeckendorf's theorem, gives every whole number its own unique 'Fibonacci fingerprint.'