# 1. Multiples of 3 and 5 (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.

**Method 1: Set, union, sum, print**

**Method 1: Set, union, sum, print****Method 2: collect, println**

**Method 2: collect, println****union :**union is still a set operation, union([1,2],[2,3])=[1,2,3], even though we apply it on arrays.**println:**print line, print the argument and start a new line.

# 2 Even Fibonacci numbers (1*)

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.

**Method 1 : while loop, append!, filter**

**Method 1 : while loop, append!, filter****while :**while loop**while**condition body**end****append**!(collection, collection2): append collection 2 to*collec**tion*,**!**indicates*collection*will takes on the new value**l****ast**(coll): getting the last element of an ordered collection**iseven**(x::Integer)**:**test whether the integer**x**is even, and gives either 0 or 1 of type*Bool***filter**(f,a::AbstractArray)**:**select elements from the array**a**base on the result of the boolean function f applying to each element of a

**Method 2 : broadcasting**

**Method 2 : broadcasting****. : broadcasting,**since A is an array, we want to broadcast the function**iseven**onto its elements**iseven**.(A): gives an*BitArray,*with elements 0 or 1, e.g.**iseven([1 2 3]) ----->[0 1 0]****A[ iseven**.(A)**] :**extract elements on positions with an 1 in the BitArray**$ :**expression interpolation

# 3 Largest prime factor (1*)

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

**Method 1 : calling package**

**Method 1 : calling package****using**package: packages can be called with thecommand**using****factor**(n::Integer) : returns the prime factorization of the integer, e.g. factor(**-**9) returns**-**1**⋅**3**^**2**collect(**collection**):**turn our collection into an array, in this case, we get an array of pairs, (*arraye，exponent).*

**Extra: package manager**

**Extra: package manager****]**

**add **package

**rm **package

**update **package

**update**

We can enter the Julia package management mode, by enter

**]**in**REPL****add**package**:**add and install package automatically**rm**package**:**remove a package**update :**update a given package, or if no name is supplied, all packages will be updated

# 4 Largest palindrome product (1*)

A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Find the largest palindrome made from the product of two 3-digit numbers.

a

**==**b: checks if a=b, and return 1 or 0We then create a multiplication table M , and

the function**broadcast**to all entries in M, and**isPalindrome**the Palindromes**select****maximum(**itr**):**find the maximum element in*itr*

**Method 2 : another way of defining a function**

**Method 2 : another way of defining a function**We can also define a function in the more "mathematical" fashion

# 5 Smallest Multiple (1*)

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.

What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

**Method 1**

**Method 1**:)

## Extra: Plots 1, Scatter

**Plots package****scatter:**scatter plot, where the vertical axis is on a log scale

# 6 Sum Square Difference

## Method 1

:)

## Extra: Plots 2, plot, labels

**I:**gives the x coordinates**A,B :**each gives a set of y coordinates

# 7 10001st prime

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10 001st prime number?

# 8 Largest product in a series

# 9 Special Pythagorean triplet

# 10 Summation of primes

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.