What’s the sum \(\frac{F_2}{F_1}+\frac{F_4}{F_2}+\frac{F_6}{F_3}+...+\frac{F_{18}}{F_9}+\frac{F_{20}}{F_{10}}\)?
Is \(F_{100}\) a multiple of \(3\)?
We have a sequence where the first term (\(x_1\)) is equal to \(2\), and each term is \(1\) minus the reciprocal of the previous term (which we can write as \(x_{n+1}=1-\frac{1}{x_n}\)).
What’s \(x_{57}\)?
Let \(n\) be a positive integer. Can \(n^7-77\) ever be a Fibonacci number?
Cut a packet of 4 cards. Is any of the cards in the same place as it was before?
We have a packet of 13 cards from Ace to King. Let Ace be the first card, 2 the second card and so on with King being the thirteenth card. How can you interchange 4 and 7 (and leave all other cards where they are) by only switching adjacent pairs of cards?
How many permutations of 13 cards leaves the third card where it started?
Does there exist an irreducible tiling with \(1\times2\) rectangles of a \(6\times 6\) rectangle?
Irreducibly tile a floor with \(1\times2\) tiles in a room that is a \(6\times8\) rectangle.