descr=%{
Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
Triangle        T_(n)=n(n+1)/2      1, 3, 6, 10, 15, ...
Pentagonal      P_(n)=n(3n−1)/2         1, 5, 12, 22, 35, ...
Hexagonal       H_(n)=n(2n−1)       1, 6, 15, 28, 45, ...

It can be verified that T_(285) = P_(165) = H_(143) = 40755.

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

# number[n]=1,2 or 3 if 3 triangular, pentagonal and hexagonal
$number={}
def save_and_verif(t)
    if $number[t].nil?
        $number[t]=1
    else
        $number[t] += 1
        if $number[t] == 3
            puts t
            exit 0
        end
    end
end

def T(n)
    t=n*(n+1)/2
    save_and_verif(t)
end
def P(n)
    t=n*(3*n-1)/2
    save_and_verif(t)
end
def H(n)
    t=n*(2*n-1)
    save_and_verif(t)
end

n=144
while true
    T(n)
    P(n)
    H(n)

    n+=1
end