일 | 월 | 화 | 수 | 목 | 금 | 토 |
---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | |||
5 | 6 | 7 | 8 | 9 | 10 | 11 |
12 | 13 | 14 | 15 | 16 | 17 | 18 |
19 | 20 | 21 | 22 | 23 | 24 | 25 |
26 | 27 | 28 | 29 | 30 | 31 |
- 정오각형
- algeomath
- 시뮬레이션
- 지오지브라
- 프로젝트 오일러
- 제곱근의뜻
- 리만합
- 피타고라스 정리
- 큰수의법칙
- Geogebra
- counting sunday
- project euler
- 프랙탈
- java
- 구분구적법
- 큰 수의 법칙
- 오일러
- 삼각함수의그래프
- 수학탐구
- 파이썬
- 재귀함수
- 확률실험
- 상합
- 작도
- 하합
- 알지오매스
- python
- 블록코딩
- 이항분포
- 몬테카를로
- Today
- Total
목록Project Euler (51)
이경수 선생님의 수학실험실
Problem 43(Sub-string divisibility) The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property. Let \(d_{1}\) be the 1st digit, \(d_{2}\) be the 2nd digit, and so on. In this way, we note the following: \(d_{2}d_{3}d_{4}=406\) is divisible by 2 \(d_{3}d_{4}d_{5}=063\..
Problem 42(Coded triangle numbers) The \( n^{th} \) term of the sequence of triangle numbers is given by, \( t_{n} = \frac{1}{2} n(n+1) \) so the first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is \(1..
Problem 41(Pandigital prime) We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime. What is the largest n-digit pandigital prime that exists? In Python: import math import time def isprime(n): if n == 0 or n == 1: return False else: for i in range(2, n): if n % i == 0: return False retu..
Problem 40(Champernowne's constant) An irrational decimal fraction is created by concatenating the positive integers: 0.123456789101112131415161718192021... It can be seen that the 12th digit of the fractional part is 1. If \(d_{n}\) represents the nth digit of the fractional part, find the value of the following expression. \(d_{1}\) × \(d_{10}\) × \(d_{100}\) × \(d_{1000}\) × \(d_{10000}\) × \..
Problem 39(Integer right triangles) If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120. {20,48,52}, {24,45,51}, {30,40,50} For which value of p ≤ 1000, is the number of solutions maximised? In Python: import time def ispythatriple(p, i, j): if i ** 2 + j ** 2 == (p - (i + j)) ** 2: return True else: return False star..
Problem 38(Pandigital multiples) Take the number 192 and multiply it by each of 1, 2, and 3: 192 × 1 = 192 192 × 2 = 384 192 × 3 = 576 By concatenating each product we get the 1 to 9 pandigital, 192384576. We will call 192384576 the concatenated product of 192 and (1,2,3) The same can be achieved by starting with 9 and multiplying by 1, 2, 3, 4, and 5, giving the pandigital, 918273645, which is ..
Problem 37(Truncatable primes) The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3. Find the sum of the only eleven primes that are both truncatable from left to right and right to left. NOTE: 2, 3, 5, a..
Problem 36(Double-base palindromes) The decimal number, \(585 = 1001001001_{2}\) (binary), is palindromic in both bases. Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. (Please note that the palindromic number, in either base, may not include leading zeros.) In Python: import math import time def ispalindrome10(n): dig = int(math.log10(n)) + 1 nSt..