Hypothesis - Neither of 5 or 13 selected

Basic information

        Balls drawn         Richard's success
# 1     03 05 14 22 30 44   two matches, one off by one
# 3     11 17 21 29 30 40   no matches
# 7     09 17 32 36 42 44   two matches, three off by four

Select three from 05 13 28 46 48

Near Misses

If 5 and 13 aren't selected, then the three near misses from lottery 7 must be:

28 46 48

These must be four off

32 42 44

respectively, so these balls cannot be matches.
From lottery 3, neither can 17 be selected. Hence, the two matches must be:

09 36

This gives the five selections:

09 28 36 46 48

Refutation

None of these five appear in lottery 1, yet Richard had two matches. This is impossible with only six balls.

Hypothesis Fails!

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