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37 seems to be the same answer several people got from different postings I did on other sites. Still not clear on how 37 was calculated. Can someone please explain in laymans terms? THX

Those marked with a * can be achieved in different ways, but 37 is the smallest number which cannot be scored from 0,1, 4, 6, 14 & 15.

0 = 0 + 0 + 0
1 = 0 + 0 + 1
2 = 0 + 1 + 1
3 = 1 + 1 + 1
4 = 0 + 0 + 4
5 = 0 + 1 + 4
6 = 0 + 0 + 6 *
7 = 0 + 1 + 6
8 = 1 + 1 + 6
9 = 1 + 4 + 4
10 = 0 + 4 + 6
11 = 1 + 4 + 6
12 = 0 + 6 + 6
13 = 1 + 6 + 6
14 = 0 + 0 + 14
15 = 0 + 0 + 15 *
16 = 0 + 1 + 15 *
17 = 1 + 1 + 15
18 = 0 + 4 + 14
19 = 1 + 4 + 14
20 = 0 + 6 + 14
21 = 1 + 6 + 14
22 = 1 + 6 + 15
23 = 4 + 4 + 15
24 = 4 + 6 + 14
25 = 4 + 6 + 15
26 = 6 + 6 + 14
27 = 6 + 6 + 15
28 = 0 + 14 + 14
29 = 0 + 14 + 15
30 = 1 + 14 + 15
31 = 1 + 15 + 15
32 = 4 + 14 + 14
33 = 4 + 14 + 15
34 = 4 + 15 + 15
35 = 6 + 14 + 15
36 = 6 + 15 + 15
37 = ?

Thanks Seamus.
Brendan answered that long before me. I didn't notice his post.