Just for fun: Countdown numbers game solver

[Arnaud Delobelle]

On Jan 20, 5:41 pm, dg.google.gro... at thesamovar.net wrote:
> Ever since I learnt to program I've always loved writing solvers for
> the Countdown numbers game problem in different languages

Ok so here's a challenge I just thought of:

What is (or are) the set of 6 starting numbers which are such that the
smallest target they can't reach is maximal?

E.g for 1, 2, 3, 4, 5, 6 the smallest target they can't reach is 284:

100 = ((5*4)*(3+2))
101 = (5+((4*3)*(6+2)))
102 = (((6*5)+4)*3)
103 = ((5*((6*4)-3))-2)
...
280 = ((5*(4+3))*(6+2))
281 = (((5*(4+3))*(6+2))+1)
282 = ((4+((6*5)*3))*(2+1))
283 = (3+(((5*4)*2)*(6+1)))
284 : can't be done

For 2, 3, 5, 8, 9, 10, the smallest unreachable target is 796 (and
there are five others: 829, 956, 961, 964, 991).

For 2, 4, 5, 8, 9, 10, the smallest is 807 (but there are 23 others)

Time to go to bed :)

--
Arnaud

PS: apologies if I got the results wrong...