In the 20×20 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 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20×20 grid?

Solution:
Function Prob011() As Long
Prob011 = 0
Dim strGrid = ""
strGrid &= " 08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08"
strGrid &= " 49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00"
strGrid &= " 81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65"
strGrid &= " 52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91"
strGrid &= " 22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80"
strGrid &= " 24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50"
strGrid &= " 32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70"
strGrid &= " 67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21"
strGrid &= " 24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72"
strGrid &= " 21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95"
strGrid &= " 78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92"
strGrid &= " 16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57"
strGrid &= " 86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58"
strGrid &= " 19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40"
strGrid &= " 04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66"
strGrid &= " 88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69"
strGrid &= " 04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36"
strGrid &= " 20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16"
strGrid &= " 20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54"
strGrid &= " 01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48"

'Diag-Right
For f As Integer = 0 To 16
Dim Val1 As Integer = 0
Dim Val2 As Integer = 0
Dim Val3 As Integer = 0
Dim Val4 As Integer = 0
Dim StartPos As Integer = (Offset * 3) + (f * CharPerLine)
Dim GroupCount As Integer = 1
While GroupCount < = 17 Val1 = CInt(strGrid.Substring(StartPos, Offset).Trim) Val2 = CInt(strGrid.Substring(StartPos + CharPerLine - Offset, Offset).Trim) Val3 = CInt(strGrid.Substring(StartPos + (CharPerLine * 2) - (Offset * 2), Offset).Trim) Val4 = CInt(strGrid.Substring(StartPos + (CharPerLine * 3) - (Offset * 3), Offset).Trim) If Val1 * Val2 * Val3 * Val4 > Prob011 Then Prob011 = Val1 * Val2 * Val3 * Val4
StartPos += Offset
GroupCount += 1
End While
Next
End Function

Summary:
I had a LOT of fun figuring out a solution to this one! I was pretty sure there was a way to use a Matrix for this, but — mainly because I can’t remember the last time I’ve actually used one — I skipped the matrix and went with a slightly less elegant way.

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

Find the sum of all the primes below two million.

Solution:
Function Prob010() As Long
For k As Integer = 2 To 2000000
If IsPrime(k) Then Prob010 += k
Next
End Function

Summary:
They are making this WAY too easy. I’m not sure if it’s just the nature of this sort of problem or whether my IsPrime routine needs some tweaking, but this problem takes the longest compared to all of the others I’ve done up to this point. Even so, it’s only 10-seconds, which is well within the target range allowed by Project Euler.

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^(2) + b^(2) = c^(2) For 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.

Solution:
Function Prob009() As Long
For a As Integer = 0 To 1000
For b As Integer = 0 To 1000
For c As Integer = 0 To 1000
If (a + b + c) = 1000 AndAlso a < b AndAlso b < c AndAlso System.Math.Pow(a, 2) + System.Math.Pow(b, 2) = System.Math.Pow(c, 2) Then Return a * b * c Next Next Next End Function

Summary:
Pretty easy...

Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Solution:
Function Prob008() As Long
Dim strInput As New System.Text.StringBuilder
strInput.Append("73167176531330624919225119674426574742355349194934")
strInput.Append("96983520312774506326239578318016984801869478851843")
strInput.Append("85861560789112949495459501737958331952853208805511")
strInput.Append("12540698747158523863050715693290963295227443043557")
strInput.Append("66896648950445244523161731856403098711121722383113")
strInput.Append("62229893423380308135336276614282806444486645238749")
strInput.Append("30358907296290491560440772390713810515859307960866")
strInput.Append("70172427121883998797908792274921901699720888093776")
strInput.Append("65727333001053367881220235421809751254540594752243")
strInput.Append("52584907711670556013604839586446706324415722155397")
strInput.Append("53697817977846174064955149290862569321978468622482")
strInput.Append("83972241375657056057490261407972968652414535100474")
strInput.Append("82166370484403199890008895243450658541227588666881")
strInput.Append("16427171479924442928230863465674813919123162824586")
strInput.Append("17866458359124566529476545682848912883142607690042")
strInput.Append("24219022671055626321111109370544217506941658960408")
strInput.Append("07198403850962455444362981230987879927244284909188")
strInput.Append("84580156166097919133875499200524063689912560717606")
strInput.Append("05886116467109405077541002256983155200055935729725")
strInput.Append("71636269561882670428252483600823257530420752963450")
Dim Group1 As Integer = 0
Dim Group2 As Integer = 0
Dim Group3 As Integer = 0
Dim Group4 As Integer = 0
Dim Group5 As Integer = 0
Dim StringPos As Integer = 0
Do While StringPos < strInput.Length - 4 Group1 = strInput.ToString.Substring(StringPos, 1) Group2 = strInput.ToString.Substring(StringPos + 1, 1) Group3 = strInput.ToString.Substring(StringPos + 2, 1) Group4 = strInput.ToString.Substring(StringPos + 3, 1) Group5 = strInput.ToString.Substring(StringPos + 4, 1) If Group1 * Group2 * Group3 * Group4 * Group5 > Prob008 Then Prob008 = Group1 * Group2 * Group3 * Group4 * Group5
StringPos += 1
Loop
End Function

Summary:
It isn’t pretty, but it works :)

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

What is the 10001^(st) prime number?

Solution:
Function Prob007() As Long
Dim k As Integer = 1
Dim PrimeCount As Integer = 0
Dim TargetPrime As Integer = 10001
While PrimeCount < = TargetPrime k += 1 If IsPrime(k) Then PrimeCount += 1
If PrimeCount = TargetPrime Then Return k
End While
End Function