Project Euler Problem 29

Problem 29

25 October 2002

Consider all integer combinations of a^b for 2 a 5 and 2 b 5:

2²=4, 2³=8, 2⁴=16, 2⁵=32
3²=9, 3³=27, 3⁴=81, 3⁵=243
4²=16, 4³=64, 4⁴=256, 4⁵=1024
5²=25, 5³=125, 5⁴=625, 5⁵=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2 a 100 and 2 b 100?

Answer: 9183

 

 

C#

 

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Numerics;

namespace ConsoleApplication1 {
    class Program {
        static void Main(string[] args) {            
            var s = new HashSet<BigInteger>();
            for (int a = 2; a <= 100; a++) {
                for (int b = 2; b <= 100; b++) {
                    s.Add(BigInteger.Pow(a, b));
                }
            }
            Console.WriteLine(s.Count);
        }
    }
}

 

Racket

 

#lang racket
(define (problem29)
  (define s (set))
  (for* ([a (in-range 2 101)]
         [b (in-range 2 101)])
    (set! s (set-add s (expt a b))))
  (displayln (set-count s)))
(problem29)