Exercism.io → Racket → Grains

grains.rkt

Use the ~#lang~ shorthand to declare the grains module.

#lang racket

The functions grains.rkt needs to export are square and total.

(provide square total)

The definition of square is simple: $\displaystyle \text{square}\ n = 2^{n - 1}$

(define (square n) (expt 2 (sub1 n)))

The total is the sum of the number of grains of wheat on every square, i.e. $\displaystyle ∑_n=1⁶⁴ 2^{n - 1}$.

\begin{align*} ∑_n=1^k 2^{n - 1} &= 2^k &- 1
∑_n=1⁶⁴ 2^{n - 1} &= 2⁶⁴ &- 1 \ \text{total} &= 2^{65 - 1} &- 1 \ &= \text{square}\ 65 &- 1 \end{align*}

(define (total) (sub1 (square 65)))