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## #1 2024-05-15 14:07:51

Keep_Relentless
Member
From: Queensland, Australia
Registered: 2024-05-05
Posts: 61

### Project Euler Problems 10-12

I am now onto Mathematica and not just Excel. The next three:

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

11. In the 20 x 20 grid below, four numbers along a diagonal line have been marked in red [I have bolded them].

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 the same direction (up, down, left, right, or diagonally) in the 20 x 20 grid?

12. 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: 1
3: 1, 3
6: 1, 2, 3, 6
10: 1, 2, 5, 10
15: 1, 3, 5, 15
21: 1, 3, 7, 21
28: 1, 2, 4, 7, 14, 28

We 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?

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

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## #2 2024-05-15 15:37:35

Keep_Relentless
Member
From: Queensland, Australia
Registered: 2024-05-05
Posts: 61

### Re: Project Euler Problems 10-12

Problem 10 done on Mathematica.

Problem 11 could be done on Excel but I think it would take annoyingly long if I'm not missing something. I'm going to go ahead and guess that it's the diagonal 89 * 94 * 97 * 87.

Edit: Problem 12 done with Mathematica. Would be very surprised if it could be done with Excel.

Edit 2: Problem 11 done on Excel.

Last edited by Keep_Relentless (2024-05-15 17:17:12)

"The most incomprehensible thing about the world is that it is comprehensible." -Albert Einstein.

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## #3 2024-05-16 21:27:11

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,857

### Re: Project Euler Problems 10-12

Keep_Relentless wrote:

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

Problem 10 done on Mathematica.

Found quite a neat 1-liner (with 4 functions) solution in M. Verified the solution in Excel.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #4 2024-05-16 23:14:43

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,857

### Re: Project Euler Problems 10-12

Keep_Relentless wrote:

Problem 12 done with Mathematica. Would be very surprised if it could be done with Excel.

Yes, I'd also be very surprised, given the huge numbers. But maybe an Excel whizz could...

I also solved it with M.

Verified the solution in Excel via a UDF that gave all the divisors, and a formula that counted the number of divisors. Both helps were found on the net. Also, I needed the triangular number from the M solution because of the huge numbers.

Last edited by phrontister (2024-05-17 23:38:57)

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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## #5 2024-05-17 00:44:31

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,857

### Re: Project Euler Problems 10-12

Keep_Relentless wrote:

Problem 11 could be done on Excel but I think it would take annoyingly long if I'm not missing something. I'm going to go ahead and guess that it's the diagonal 89 * 94 * 97 * 87.

That's what I got, using Excel.

Copy/paste into Excel via the Wizard refused to work, but first pasting into Notepad++ and then copy/paste from there woke the Wizard up, and the grid copied over properly with the numbers in their respective cells.

That helped greatly with finding the solution via formulas that I could copy/drag with the fill handle.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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