Determining fourth number - given 5, 13 and 44

Basic information

        Balls drawn         Richard's success
# 4     26 35 38 43 47 49   second ticket: two matches, one off by three
# 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
# 9     07 17 23 32 38 42   one match

Number 5 13 and 44 selected
Choose one from 28 46
Choose one from 36 42

Lemma - 46 is selected

This requires 42 to be used as a near miss (lottery 7), so this cannot also be used as a match. Hence 36 must be selected, giving:

5 13 36 44 46

Lottery 5 has one near miss still to be determined, being four off the numbers drawn. Ignoring the exact matches, the possibilities for this are:

7 10 18 34 42

The lemma prevents the use of 42, so the only one of these that also provides a match in lottery 9 is 7. This gives a full selection of:

5 7 13 36 44 46

It is probable that Richard would have regarded 7 as being two off 9, rather than four off 3, but that's not really sufficient to rule it out.

However, there is one piece of information that I haven't used yet.

Second ticket

For lottery 4, Richard bought a second ticket, with numbers one greater than his normal choices. This would give the numbers:

6 8 14 37 45 47

This only gives one match, rather than the two Richard claimed.

Lemma Fails!

Hence

If 46 is not selected, then 28 must be. We now know:

5 13 28 44
either 36 or 42

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