Charlie Pan's Blog

Problem 1:If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.Find the sum of all the multiples of 3 or 5 below 1000.

Problem 41:We shall say that an n-digit number is pandigital if it makes use of all the digits 1 ton exactly once. For example, 2143 is a 4-digit pandigital and is also prime.What is the lar

Problem 36:The decimal number, 585 = 10010010012 (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.(Pleas

Project 31:In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).It is possible to

Problem 26:A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:1/2= 0.51/3= 0.(3)1/4

Problem 16:215 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26.What is the sum of the digits of the number 21000?

Problem 11:In the 2020 grid below, four numbers along a diagonal line have been marked in red.08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 0849 49 99 40 17 81 18 57 60 87 17 40 9

Problem 21:Let d(n) be defined as the sum of proper divisors of n (numbers less thann which divide evenly into n).If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and

Problem 6:The sum of the squares of the first ten natural numbers is,12 + 22 + ... + 102 = 385The square of the sum of the first ten natural numbers is,(1 + 2 + ... + 10)2 = 552 = 3025

Problem 46:It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.9 = 7 + 21215 = 7 + 22221 = 3 + 23225 = 7 + 232