All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Maximal number of solutions (Posted on 2018-12-08)
If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximized?

Source: Project Euler

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Basic language solution Comment 5 of 5 |
In the below, the lines

If p = 840 Then
Text1.Text = Text1.Text & Str(sm) & Str(lg) & Str(h) & crlf
End If

were added after the second part found the highest was uniquely 840.

The result of those line is the first part of the ultimate output:

240 252 348
210 280 350
168 315 357
140 336 364
120 350 370
105 360 375
56 390 394
40 399 401
24 1
30 1
36 1
40 1
48 1
56 1
60 2
84 2
90 2
120 3
168 3
180 3
240 4
360 4
420 5
660 5
720 6
840 8

where the second part is the new highest value as triangles were tested with ever increasing larger perimeters and within that increasing larger legs.

Max = 1

For p = 15 To 1000
For lg = 1 To p / 2
For sm = 1 To lg
DoEvents
h = p - lg - sm
If h < lg Then Exit For
If sm * sm + lg * lg = h * h Then
ct(p) = ct(p) + 1
If p = 840 Then
Text1.Text = Text1.Text & Str(sm) & Str(lg) & Str(h) & crlf
End If
End If
Next
Next lg
Next p
For i = 1 To 1000
If ct(i) >= Max Then
Text1.Text = Text1.Text & i & Str(ct(i)) & crlf
Max = ct(i)
End If
Next

 Posted by Charlie on 2018-12-09 10:13:45

 Search: Search body:
Forums (0)