[Project Euler]Problem 45

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

Triangle
Tn=n(n+1)/2
1, 3, 6, 10, 15, ...

Pentagonal
Pn=n(3n1)/2
1, 5, 12, 22, 35, ...

Hexagonal
Hn=n(2n1)
1, 6, 15, 28, 45, ...

It can be verified that T285 = P165 = H143 = 40755.

Find the next triangle number that is also pentagonal and hexagonal.

 

找出下一個數既是三角數又是五角數，而且還是六角數。

這道題有了上一題的經驗就解的比較容易了

t = [i*(i+1)//2 for i in range(286, 1000001)]p = [i*(3*i-1)//2 for i in range(166, 1000001)]st = set(t)sp = set(p)n = 144while True:    h = n*(2*n - 1)    if h in st and h in sp:        print(h)        break    else:        n += 1

 

速度很快，基本0.s就出來。