Problem 33 Digit canceling fractions
Problem 33: Digit cancelling fractions
The fraction 49/98 is a curious fraction, as an inexperienced mathematici[……]
Problem 32 Pandigital products
Problem 32: Pandigital products
We shall say that an n-digit number is pandigital if it makes use of all the dig[……]
Problem 31 Coin sums
Problem 31: Coin sums
In the United Kingdom the currency is made up of pound (£) and pence (p). There are eight[……]
Problem 30 Digit fifth powers
Problem 30: Digit fifth powers
Surprisingly there are only three numbers that can be written as the sum of fourt[……]
Problem 29 Distinct powers
Problem: Distinct powers
nsider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:
- 22=4, 23=8, 24=16,[……]
Problem 28 Number spiral diagonals
Problem 28: Number spiral diagonals
Starting with the number 1 and moving to the right in a clockwise direction[……]
Problem 27 Quadratic primes
Problem 27: Quadratic primes
Euler discovered the remarkable quadratic formula:
n² + n + 41
It turns out that the formula will produce 40 primes for t[……]
Problem 26 Reciprocal cycles
Problem 26: Reciprocal cycles
分析
1/6 = 0.1(6) 表示0.16666…，拥有 1 位数字的重复周期
1/7=0.(142857) 拥有6位的重复周期
找到d < 1000,[……]
Problem 25 1000-digit Fibonacci number
Problem 25: 1000-digit Fibonacci number
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn−1 + Fn−2, where F1 = 1 and F2= 1.
Hence[……]
Problem 24 Lexicographic permutations
Problem 24: Lexicographic permutations
A permutation is an ordered arrangement of objects. For example, 3124 is[……]
Problem 23 Non-abundant sums
Problem 23: Non-abundant sums
A perfect number is a number for which the sum of its proper divisors is exactly e[……]
Problem 22 Names scores
Problem 22: Names scores
Using names.txt (right click and ‘Save Link/Target As…’), a 46K text file containing[……]
Problem 21 Amicable numbers
Problem 21: Amicable numbers
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which d[……]
Problem 20 Factorial digit sum
Problem 20: Factorial digit sum
n! means n × (n − 1) × … × 3 × 2 × 1
For example, 10! = 10 × 9 × … × 3 × 2 ×[……]
Problem 19 Counting Sundays
Problem 19: Counting Sundays
You are given the following information, but you may prefer to do some research for[……]