Lemma - 44 is selected

Basic information

        Balls drawn         Richard's success
# 3     11 17 21 29 30 40   no matches
# 4     26 35 38 43 47 49   no matches
# 5     03 05 09 13 14 38   two matches, one off by four
# 7     09 17 32 36 42 44   two matches, three off by four
# 8     02 05 21 22 25 32   one match
# 9     07 17 23 32 38 42   one match

Select two from 28 46 48

Lottery 7

Because 44 is selected, this means 48 cannot be used for a near miss. The near misses must therefore be 28 and 46. This gives the following selections:

[5 or 13] 28 44 46

Lottery 7 needs one more exact match (apart from 44). This cannot be 17 (from lottery 3), and both 32 and 42 are used for the near misses. The exact match must therefore be either 9 or 36.

Lottery 9

Richard cannot have 17 and 38 (from lotteries 3 and 4). The near misses in lottery 7 rule out 32 or 42.
Hence he must have one of 7 or 23. This gives:

[5 or 13] [7 or 23] [9 or 36] 28 44 46

Refutation

Lottery 8 requires 5 (rather than 13) to be selected. This gives 5 and 9 as the two matches in lottery 5. However, 5 was chosen as a near miss from 9 (lottery 7), so Richard cannot have both.

Lemma Fails!

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