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
(In reply to
Another method by broll)
1st: Could you please explain your formula a little? Is a=(u-v) and b=(u+b). Even if so, I do not follow - thanks!
2nd: the correspondence with A002182 is not strict:
If you compare the number of solutions for record holding perimeters, or record breaking perimeter values, neither list strictly follow A002182.
record holders
# of equal perimeters perimeters
1 12
1 24
1 30
1 36
1 40
1 48
1 56
2 60
2 84
2 90
3 120
3 168
3 180
4 240
4 360
5 420
5 660
6 720
8 840
8 1260
10 1680
12 2520
13 4620
16 5040
20 9240
29 11969
or record breakers
2 60
3 120
4 240
5 420
6 720
8 840
10 1680
12 2520
13 4620
16 5040
20 9240
29 11969
A002182:
…, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120
Thanks!
SL
(ps - I hope I have these right - I must still check further.)
Edited on December 9, 2018, 4:00 am
trying to understand...
