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neat way to program minimum of sum


Hi
I need to program the following function:

f(t) = max{n>0 : X1 + ... + Xn > t}

where Xi are some random numbers. I've done it using Module and Wile:

x[i_]:=x[i]=Random[]
f[t_]:=f[t]=Module[{i}, i=1; While[Total[Array[x, i]]<=t, i++]; Return[i-1]];

This works but requires Module and three instructions within. Can it
be simplified to a true one-liner, preferably with some functional
programming trick?

Thanks in advance,
P. Kaminski


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