ホーム - Project Euler

Problem 9¶

Special Pythagorean Triplet¶

A Pythagorean triplet is a set of three natural numbers, $a \lt b \lt c$, for which,
$$a^2 + b^2 = c^2.$$
For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.
There exists exactly one Pythagorean triplet for which $a + b + c = 1000$.
Find the product $abc$.

特別なピタゴラス数¶

ピタゴラス数(ピタゴラスの定理を満たす自然数)とは a < b < c で以下の式を満たす数の組である.
$$a^2 + b^2 = c^2.$$
例えば, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$ である.
a + b + c = 1000 となるピタゴラスの三つ組が一つだけ存在する.
これらの積 abc を計算しなさい.

#!r6rs
#!chezscheme

(import (chezscheme))

(define answer-9
  (let loop1 ([a 1])
    (if (< 333 a)
      (error "answer-9" "answer-9 was not found!")
      (let loop2 ([b a])
        (if (< 499 b)
          (loop1 (add1 a))
          (let ([c (- 1000 a b)])
            (if (= (+ (expt a 2)
                      (expt b 2))
                   (expt c 2))
              (* a b c)
              (loop2 (add1 b)))))))))

(printf "9: ~D~%" answer-9)