Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.6 AIME Find the answer United States

Problem:

The Lucas numbers are defined by $L_{0} = 2$ , $L_{1} = 1$ , and $L_{n+2} = L_{n+1} + L_{n}$ for every $n \geq 0$ . There are $N$ integers $1 \leq n \leq 2016$ such that $L_{n}$ contains the digit $1$ . Estimate $N$ .

An estimate of $E$ earns $\lfloor 20 - 2|N - E| \rfloor$ or $0$ points, whichever is greater.

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

lucas_ones $\text{n = length filter ( elem '1') take (n+1) lucas strs}$

where

$\text{lucas} = 2 : 1 : \text{zipWith}~(+)~\text{lucas}~(\text{tail}~\text{lucas})$

$\text{lucas strs = map show lucas}$

$\text{main = putStrLn show lucas ones 2016}$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.