Project Euler is a website set up with a wide selection of math problems. While some, if not all of them, could be figured out manually over time you could be looking at taking weeks or months to find an answer.
The idea is that you use any form of coumputer programming you are happy with to create a programme that returns the answer. The challenge is knowing how to structure and write the programme to complete the task at hand. When done correctly a computer can return the answer instantly or in seconds.
The puzzles can all be found at https://projecteuler.net and if you create an account you can select a puzzle and check if you answer is correct.
The following are just my methods I used to clear some of the puzzles on the website and there are no doubt better, cleaner ways to get to the same outcome. I'm not posting the answers here but they are all tested and verified before uploading.
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.
Sub Problem1() Dim Answer As Long Answer = 0 For x = 1 To 999 If ((x / 3) - Int((x / 3))) = 0 Or ((x / 5) - Int((x / 5))) = 0 Then Answer = Answer + x Else Answer = Answer End If Next MsgBox Answer End Sub
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.
Sub Problem2() Dim Answer As Long Dim x As Long Dim y As Long Dim z As Long Answer = 0 x = 0 y = 1 Do While z < 4000000 z = x + y If ((z / 2) - Int(z / 2)) = 0 Then Answer = Answer + z End If x = y y = z Loop MsgBox Answer End Sub
The prime factors of 13195 are 5, 7, 13 and 29.What is the largest prime factor of the number 600851475143 ?
On this one I did create a way to calculate the answer but due to limitations with integer values in VBA running the answer for the actual problem generates an overflow error. As such when I knew that the solution I made worked I ran a quick python script to generate the correct answer (also below).
Dim Answer As Long Dim Factors As Integer Dim Number As Integer Dim x As Long Dim y As Long Answer = 0 Factors = 0 Number = 13195 Do While Answer = 0 For y = Number To y = 1 Step -1 For x = 1 To Number If y Mod x = 0 Then Factors = Factors + 1 End If Next x If Factors = 2 And Number Mod y = 0 Then Answer = y Exit For Else Factors = 0 End If Next y Loop MsgBox Answer
Number = 600851475143 x = 2 while x * x < Number: while Number % x == 0: Number = Number / x x = x + 1 print (Number)
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.
Sub Problem4() Dim Answer As Long Dim Working As Long Dim Highest As Long Dim x As Long Dim y As Long Dim LeftNum As String Dim RightNum As String Answer = 0 Working = 0 Highest = 0 x = 999 y = 999 Do While Answer = 0 And x > 1 And y > 1 Working = x * y LeftNum = Left(Working, 3) RightNum = Right(Working, 3) If LeftNum = StrReverse(RightNum) Then If Working > Highest Then Highest = Working x = 999 y = y - 1 ElseIf Highest > Working Then Highest = Highest x = 999 y = y - 1 End If End If x = x - 1 Loop Answer = Highest MsgBox Answer End Sub
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?
Sub Problem5() Dim Answer As Long Dim x As Long Dim y As Long Answer = 0 x = 10 y = 1 Do While Answer = 0 If ((x / y) - Int(x / y)) = 0 Then If y = 20 Then Answer = x Else y = y + 1 End If Else x = x + 1 y = 1 End If Loop MsgBox Answer End Sub
The sum of the squares of the first ten natural numbers is,1 2 + 2 2 + ... + 10 2 = 385The square of the sum of the first ten natural numbers is,(1 + 2 + ... + 10) 2 = 55 2 = 3025Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
Sub Problem6() Dim Answer As Long Dim x As Long Dim Working1 As Long Dim Working2 As Long Answer = 0 x = 1 Working1 = 0 Working2 = 0 For x = 1 To 100 Working1 = Working1 + (x ^ 2) Working2 = Working2 + x Next Working2 = Working2 ^ 2 Answer = Working2 - Working1 MsgBox Answer End Sub
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?
Sub Problem7() Dim Answer As Long Dim Number As Long Dim Working As Long Dim Factors As Long Dim x As Long Dim y As Long Answer = 0 Number = 10001 Working = 0 Factors = 0 y = 2 Do While Working < Number For x = 1 To y If y Mod x = 0 Then Factors = Factors + 1 End If Next x If Factors = 2 Then Answer = y Working = Working + 1 End If y = y + 1 Factors = 0 Loop MsgBox Answer End Sub
The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832. 73167176531330624919225119674426574742355349194934 96983520312774506326239578318016984801869478851843 85861560789112949495459501737958331952853208805511 12540698747158523863050715693290963295227443043557 66896648950445244523161731856403098711121722383113 62229893423380308135336276614282806444486645238749 30358907296290491560440772390713810515859307960866 70172427121883998797908792274921901699720888093776 65727333001053367881220235421809751254540594752243 52584907711670556013604839586446706324415722155397 53697817977846174064955149290862569321978468622482 83972241375657056057490261407972968652414535100474 82166370484403199890008895243450658541227588666881 16427171479924442928230863465674813919123162824586 17866458359124566529476545682848912883142607690042 24219022671055626321111109370544217506941658960408 07198403850962455444362981230987879927244284909188 84580156166097919133875499200524063689912560717606 05886116467109405077541002256983155200055935729725 71636269561882670428252483600823257530420752963450 Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?
Sub Problem8() Dim Answer As String Dim Working As String Dim TestString As String Dim AdjNum As Integer Dim x As Integer Dim y As Integer Answer = 0 Working = 1 AdjNum = 13 TestString = "73167176531330624919225119674426574742355349194934969835203127745063262395783180169848018694788518438586156078911294949545950173795833195285320880551112540698747158523863050715693290963295227443043557668966489504452445231617318564030987111217223831136222989342338030813533627661428280644448664523874930358907296290491560440772390713810158593079608667017242712188399879790879227492190169972088809377665727333001053367881220235421809751254540594752243525849077116705560136048395864467063244157221553975369781797784617406495514929086256932197846862248283972241375657056057490261407972968652414535100474821663704844031998900088952434506585412275886668811642717147992444292823063465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" For y = 1 To (999 - AdjNum) For x = 0 To (AdjNum - 1) Working = Mid(TestString, (y + x), 1) * Working Next x If Working + 0 > Answer Then Answer = Working End If Working = 1 Next y MsgBox Answer
A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,a 2 + b 2 = c 2For example, 3 2 + 4 2 = 9 + 16 = 25 = 5 2.There exists exactly one Pythagorean triplet for which a + b + c = 1000.Find the product abc.
Sub Problem9() Dim Answer As Long Dim x As Long Dim a As Long Dim b As Long Dim c As Long For a = 1 To 1000 For b = 1 To 1000 c = (a ^ 2) + (b ^ 2) If (Sqr(c) - Int(Sqr(c))) = 0 Then x = a + b + Sqr(c) If x = 1000 Then Answer = a * b * Sqr(c) Exit For End If End If Next b If Answer > 0 Then Exit For End If Next a MsgBox Answer End Sub
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.Find the sum of all the primes below two million.
This one could do with some level of rework before I would be happy with it as it took a little over 8 mins to run all around and I like to keep them under the minute mark as per the website guidelines. I mean it still works but there is obviously a cleaner way to do this.
Sub Problem10() Dim Answer As String Dim Factors As Long Dim Number As Long Dim x As Long Dim y As Long Answer = "0" Factors = 0 Number = 2000000 y = 2 Do While y < Number For x = 1 To y If y Mod x = 0 Then Factors = Factors + 1 If Factors = 3 Then Exit For End If End If Next x If Factors = 2 Then Answer = (Answer + 0) + (x - 1) End If Factors = 0 y = y + 1 Loop MsgBox Answer End Sub
Still working on it :)
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...Let us list the factors of the first seven triangle numbers:1: 13: 1,36: 1,2,3,610: 1,2,5,1015: 1,3,5,1521: 1,3,7,2128: 1,2,4,7,14,28We can see that 28 is the first triangle number to have over five divisors.What is the value of the first triangle number to have over five hundred divisors?
No doubt this one is a brute force effort and takes far to long to run repeatedly but it does give the correct soultion. Thinking again I could have it account for the square root of each triangle number and stop attempting to divide each number for factors when it crosses that point which should save time when working with such high numbers.
Sub Problem12() Dim Answer As String Dim Factors As Long Dim x As Long Dim y As Long Dim z As Long Answer = "0" Factors = 0 y = 1 z = 1 Do While Answer = 0 y = (z * (z + 1)) / 2 For x = 1 To y If y Mod x = 0 Then Factors = Factors + 1 End If Next x If Factors > 500 Then Answer = y Exit Do End If Factors = 0 z = z + 1 Loop MsgBox Answer End Sub