Project Euler

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# [[Problem 15]]

## Lattice Paths

Starting in the top left corner of a $2 \times 2$ grid, and only being able to move to the right and down, there are exactly $6$ routes to the bottom right corner.

![](0015.png)

How many such routes are there through a $20 \times 20$ grid?

## 格子経路

2×2 のマス目の左上からスタートした場合, 引き返しなしで右下にいくルートは 6 つある.

![](0015.png)

では, 20×20 のマス目ではいくつのルートがあるか.

```scheme

#!r6rs

#!chezscheme

(import (chezscheme))

(define iota-40-20

  (filter

    (lambda (num)

      (< 20 num))

    (iota 41)))

(define iota-20-1

  (cdr (iota 21)))

(define answer-15

  (/ (apply * iota-40-20)

     (apply * iota-20-1)))

(printf "15: ~D~%" answer-15)

```